Sequences

392,541 sequences

Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime.A024161
Number of integer-sided triangles with sides a,b,c, a < b < c, a+b+c = n such that a,b,c are pairwise relatively prime.
Number of incongruent integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that gcd(a,b,c)=1.A024162
Number of incongruent integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that gcd(a,b,c)=1.
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b < b - a.A024163
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b < b - a.
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b = b - a.A024164
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b = b - a.
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b > b - a.A024165
Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b > b - a.
a(n) = Sum_{1 <= i < j <= n} (j-i)^3.A024166
a(n) = Sum_{1 <= i < j <= n} (j-i)^3.
a(n) = n!*(1 - 1/2 + 1/3 - ... + c/n), where c = (-1)^(n+1).A024167
a(n) = n!*(1 - 1/2 + 1/3 - ... + c/n), where c = (-1)^(n+1).
a(n) = n! * (1 + Sum_{j=1..n} (-1)^j/j).A024168
a(n) = n! * (1 + Sum_{j=1..n} (-1)^j/j).
Integer part of ((2nd elementary symmetric function of 1,2,...,n)/(1+2+...+n)).A024169
Integer part of ((2nd elementary symmetric function of 1,2,...,n)/(1+2+...+n)).
Expansion of 1/((1-x)(1-6x)(1-9x)(1-10x)).A024170
Expansion of 1/((1-x)(1-6x)(1-9x)(1-10x)).
Integer part of ((4th elementary symmetric function of 1,2,...,n)/(1+2+...+n)).A024171
Integer part of ((4th elementary symmetric function of 1,2,...,n)/(1+2+...+n)).
Integer part of ((3rd elementary symmetric function of 1,2,..,n)/(2nd elementary symmetric function of 1,2,...,n)).A024172
Integer part of ((3rd elementary symmetric function of 1,2,..,n)/(2nd elementary symmetric function of 1,2,...,n)).
Integer part of ((4th elementary symmetric function of 1,2,..,n)/(2nd elementary symmetric function of 1,2,...,n)).A024173
Integer part of ((4th elementary symmetric function of 1,2,..,n)/(2nd elementary symmetric function of 1,2,...,n)).
a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).A024174
a(n) is floor((4th elementary symmetric function of 1,2,..,n)/(3rd elementary symmetric function of 1,2,...,n)).
Expansion of g.f. (x^3 - 6*x^2 + 5*x - 1)/((2*x - 1)*(2*x^2 - 4*x + 1)).A024175
Expansion of g.f. (x^3 - 6*x^2 + 5*x - 1)/((2*x - 1)*(2*x^2 - 4*x + 1)).
a(n) = (n+2)!(1/3 - 1/4 + ... + c/(n+2)), where c=(-1)^(n+1).A024176
a(n) = (n+2)!(1/3 - 1/4 + ... + c/(n+2)), where c=(-1)^(n+1).
a(n) = floor ( (2nd elementary symmetric function of 2,3,...,n+2)/(2+3+...+n+2) ).A024177
a(n) = floor ( (2nd elementary symmetric function of 2,3,...,n+2)/(2+3+...+n+2) ).
a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3)).A024178
a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3)/(2+3+...+n+3)).
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2+3+...+n+4)).A024179
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2+3+...+n+4)).
a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3) / (2nd elementary symmetric function of 2,3,...,n+3) ).A024180
a(n) = floor((3rd elementary symmetric function of 2,3,...,n+3) / (2nd elementary symmetric function of 2,3,...,n+3) ).
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2nd elementary symmetric function of 2,3,...,n+4)).A024181
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(2nd elementary symmetric function of 2,3,...,n+4)).
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(3rd elementary symmetric function of 2,3,...,n+4)).A024182
Integer part of ((4th elementary symmetric function of 2,3,...,n+4)/(3rd elementary symmetric function of 2,3,...,n+4)).
Second elementary symmetric function of 3,4,...,n+3.A024183
Second elementary symmetric function of 3,4,...,n+3.
Third elementary symmetric function of 3,4,...,n+4.A024184
Third elementary symmetric function of 3,4,...,n+4.
Fourth elementary symmetric function of 3,4,...,n+5.A024185
Fourth elementary symmetric function of 3,4,...,n+5.
Expansion of Molien series for 8-dimensional real Clifford group 2^{1+6}.Alt_8.2 of genus 3 and order 5160960.A024186
Expansion of Molien series for 8-dimensional real Clifford group 2^{1+6}.Alt_8.2 of genus 3 and order 5160960.
n-th elementary symmetric function of 3,4,...,n+3.A024187
n-th elementary symmetric function of 3,4,...,n+3.
a(n) = ((n+2)!/2)(1/3 - 1/4 + ... + c/(n+2)), where c = (-1)^(n+1).A024188
a(n) = ((n+2)!/2)(1/3 - 1/4 + ... + c/(n+2)), where c = (-1)^(n+1).
a(n) = ((n+3)!/2)*Sum_{k=1..n} (-1)^(k+1)/(k+3).A024189
a(n) = ((n+3)!/2)*Sum_{k=1..n} (-1)^(k+1)/(k+3).
[ (2nd elementary symmetric function of 3,4,...,n+3)/(3+4+...+n+3) ].A024190
[ (2nd elementary symmetric function of 3,4,...,n+3)/(3+4+...+n+3) ].
[ (3rd elementary symmetric function of 3,4,...,n+4)/(3+4+...+n+4) ].A024191
[ (3rd elementary symmetric function of 3,4,...,n+4)/(3+4+...+n+4) ].
Integer part of (4th elementary symmetric function of 3,4,...,n+5)/(3+4+...+n+5).A024192
Integer part of (4th elementary symmetric function of 3,4,...,n+5)/(3+4+...+n+5).
Integer part of (3rd elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+4}.A024193
Integer part of (3rd elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+4}.
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)) ], where S(n) = {3,4, ..., n+5}.A024194
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric of S(n)) ], where S(n) = {3,4, ..., n+5}.
Integer part of (4th elementary symmetric function of S(n))/(3rd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+5}.A024195
Integer part of (4th elementary symmetric function of S(n))/(3rd elementary symmetric of S(n)), where S(n) = {3,4, ..., n+5}.
a(n) = 2nd elementary symmetric function of the first n+1 odd positive integers.A024196
a(n) = 2nd elementary symmetric function of the first n+1 odd positive integers.
a(n) = 3rd elementary symmetric function of the first n+2 odd positive integers.A024197
a(n) = 3rd elementary symmetric function of the first n+2 odd positive integers.
4th elementary symmetric function of the first n+3 odd positive integers.A024198
4th elementary symmetric function of the first n+3 odd positive integers.
a(n) = (2n-1)!! * Sum_{k=0..n-1}(-1)^k/(2k+1).A024199
a(n) = (2n-1)!! * Sum_{k=0..n-1}(-1)^k/(2k+1).
a(0) = 1, a(1) = 0, a(n+1) = 2*a(n) + (2*n-1)^2*a(n-1).A024200
a(0) = 1, a(1) = 0, a(n+1) = 2*a(n) + (2*n-1)^2*a(n-1).
[ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 odd positive integers}.A024201
[ (2nd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+1 odd positive integers}.
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.A024202
a(n) = [ (3rd elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 odd positive integers}.A024203
[ (4th elementary symmetric function of S(n))/(first elementary symmetric function of S(n)) ], where S(n) = {first n+3 odd positive integers}.
[ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.A024204
[ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 odd positive integers}.
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 odd positive integers}.A024205
[ (4th elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+3 odd positive integers}.
Expansion of x^2*(1+x-x^2)/((1-x^2)*(1-x)^2).A024206
Expansion of x^2*(1+x-x^2)/((1-x^2)*(1-x)^2).
Number of terms in n-th derivative of a function composed with itself 7 times.A024207
Number of terms in n-th derivative of a function composed with itself 7 times.
Number of terms in n-th derivative of a function composed with itself 8 times.A024208
Number of terms in n-th derivative of a function composed with itself 8 times.
Number of terms in n-th derivative of a function composed with itself 9 times.A024209
Number of terms in n-th derivative of a function composed with itself 9 times.
Number of terms in n-th derivative of a function composed with itself 10 times.A024210
Number of terms in n-th derivative of a function composed with itself 10 times.