Sequences

Short leg of more than one primitive Pythagorean triangle.

Ordered Stirling numbers s(n,k) of the second kind.

Positions of odd numbers in A024412.

Positions of even numbers in A024412.

Position of max{s(n,k): k=1,2,...,n} in A024412, n >= 1, where s(n,k) = Stirling numbers of the second kind.

a(n) = position of next-to-largest s(n,k), for k=1,2,...,n, in A024412, n >= 3, where s(n,k) = Stirling numbers of the second kind.

s(n,a(n)) = max{s(n,k): k=1,2,...,n}, n >= 1, where s(n,k) = Stirling numbers of the second kind.

a(n) = t mod s(n,n-1), where t = max{s(n,k): k=1,2,...,n}, s(n,k) = Stirling numbers of the second kind.

a(n) = n! (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,[ n/2 ])).

a(n) = n! * Sum_{j=0..floor(n/2)} (-1)^j/binomial(n,j).

a(n) = n!*(1/C(n,0) - 1/C(n,1) - ... - 1/C(n,[ n/2 ])).

a(n) = floor(Sum_{m=1..n} Stirling2(n,m) / binomial(n-1,m-1)).

Sum of [ S(n,m)/C(n-1,m-1) ] for m = 1,2,...,n; S(n,m) are Stirling numbers of second kind.

a(n) = greatest residue of S(n,m) mod C(n-1,m-1), for m = 1,2,...,n; S(n,m) are Stirling numbers of second kind.

[ max{S(n,m)}/max{C(n-1,m-1)} ] for m = 1,2,...,n; S(n,m) are Stirling numbers of second kind.

a(n) = floor((1/n)*(S(n,1) + S(n,2) + ... + S(n,n))), where S(i,j) are Stirling numbers of second kind.

S(n,1) + S(n-1,2) + S(n-2,3) + ... + S(n+1-k,k), where k = floor((n+1)/2) and S(i,j) are Stirling numbers of the second kind.

S(n,n) + S(n-1,n-2) + S(n-2,n-4) + ... + S(n-k+1,n-2k+2), where k = [ (n+1)/2 ] and S(i,j) are Stirling numbers of second kind.

Expansion of e.g.f. sinh(exp(x)-1).

Expansion of e.g.f. cosh(exp(x)-1).

A generalized difference set on the set of all integers (lambda = 1).

a(n) = t(1) - t(2) + t(3) + ... + c*t(n), where c = (-1)^(n+1) and t(j) are Stirling numbers S(n,k) in decreasing order, for k = 1,2,...,n.

a(n) = difference between greatest two Stirling numbers S(n,k) of second kind, for k = 1,2,...,n.

Expansion of 1/((1-x)(1-6x)(1-10x)(1-11x)).

Expansion of 1/((1-x)(1-6x)(1-10x)(1-12x)).

Expansion of 1/((1-x)(1-6x)(1-11x)(1-12x)).

Expansion of 1/((1-x)(1-7x)(1-8x)(1-9x)).

Expansion of 1/((1-x)(1-7x)(1-8x)(1-10x)).

Expansion of 1/((1-x)(1-7x)(1-8x)(1-11x)).

Expansion of 1/((1-x)(1-7x)(1-8x)(1-12x)).

Expansion of 1/((1-x)(1-7x)(1-9x)(1-10x)).

Expansion of 1/((1-x)(1-7x)(1-9x)(1-11x)).

Expansion of 1/((1-x)(1-7x)(1-9x)(1-12x)).

Expansion of 1/((1-x)(1-7x)(1-10x)(1-11x)).

Expansion of 1/((1-x)*(1-7*x)*(1-10*x)*(1-12*x)).

Expansion of 1/((1-x)(1-7x)(1-11x)(1-12x)).

Sum of the products of the primes taken 2 at a time from the first n primes.

a(n) = 3rd elementary symmetric function of the first n+2 primes.

4th elementary symmetric function of the first n+3 primes.

Sum of squares of the first n primes.

a(n) is the numerator of Sum_{i = 1..n} 1/prime(i).

a(n) = [ (2nd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {first n+1 primes}.

a(n) = [ (3rd elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {first n+2 primes}.

[ (4th elementary symmetric function of P(n))/(first elementary symmetric function of P(n)) ], where P(n) = {first n+3 primes}.

[ (3rd elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {first n+2 primes}.

[ (4th elementary symmetric function of P(n))/(2nd elementary symmetric function of P(n)) ], where P(n) = {first n+3 primes}.

[ (4th elementary symmetric function of P(n))/(3rd elementary symmetric function of P(n)) ], where P(n) = {first n+3 primes}.

a(n) = s(1)*s(n) + s(2)*s(n-1) + ... + s(k)*s(n+1-k), where k = floor((n+1)/2), s = (Fibonacci numbers).

a(n) = s(1)*t(n) + s(2)*t(n-1) + ... + s(k)*t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (Lucas numbers).

a(n) = s(1)t(n) + s(2)t(n-1) + ... + s(k)t(n+1-k), where k = [ (n+1)/2 ], s = (Fibonacci numbers), t = (1, p(1), p(2), ...).