Sequences

392,541 sequences

a(n) = n!*n*(n-1)*(n-2)/36.A001810
a(n) = n!*n*(n-1)*(n-2)/36.
Coefficients of Laguerre polynomials.A001811
Coefficients of Laguerre polynomials.
Coefficients of Laguerre polynomials.A001812
Coefficients of Laguerre polynomials.
Quadruple factorial numbers: a(n) = (2n)!/n!.A001813
Quadruple factorial numbers: a(n) = (2n)!/n!.
Coefficient of H_2 when expressing x^{2n} in terms of Hermite polynomials H_m.A001814
Coefficient of H_2 when expressing x^{2n} in terms of Hermite polynomials H_m.
a(n) = binomial(n,2) * 2^(n-1).A001815
a(n) = binomial(n,2) * 2^(n-1).
Coefficients of x^n in Hermite polynomial H_{n+4}.A001816
Coefficients of x^n in Hermite polynomial H_{n+4}.
G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).A001817
G.f.: Sum_{n>0} x^n/(1-x^(3n)) = Sum_{n>=0} x^(3n+1)/(1-x^(3n+1)).
Squares of double factorials: (1*3*5*...*(2n-1))^2 = ((2*n-1)!!)^2.A001818
Squares of double factorials: (1*3*5*...*(2n-1))^2 = ((2*n-1)!!)^2.
Central factorial numbers: second right-hand column of triangle A008955.A001819
Central factorial numbers: second right-hand column of triangle A008955.
Central factorial numbers: 2nd subdiagonal of A008955.A001820
Central factorial numbers: 2nd subdiagonal of A008955.
Central factorial numbers: 3rd subdiagonal of A008955.A001821
Central factorial numbers: 3rd subdiagonal of A008955.
Expansion of Sum_{n>=0} x^(3n+2)/(1-x^(3n+2)).A001822
Expansion of Sum_{n>=0} x^(3n+2)/(1-x^(3n+2)).
Central factorial numbers: column 2 in triangle A008956.A001823
Central factorial numbers: column 2 in triangle A008956.
Central factorial numbers: 1st subdiagonal of A008956.A001824
Central factorial numbers: 1st subdiagonal of A008956.
Central factorial numbers: 2nd subdiagonal of A008956.A001825
Central factorial numbers: 2nd subdiagonal of A008956.
Number of divisors of n of the form 4k+1.A001826
Number of divisors of n of the form 4k+1.
Related to graded partially ordered sets.A001827
Related to graded partially ordered sets.
Related to graded partially ordered sets.A001828
Related to graded partially ordered sets.
Related to graded partially ordered sets.A001829
Related to graded partially ordered sets.
Related to graded partially ordered sets.A001830
Related to graded partially ordered sets.
Number of labeled graded partially ordered sets with n elements of height at most 1.A001831
Number of labeled graded partially ordered sets with n elements of height at most 1.
Number of labeled connected bipartite graphs on n nodes.A001832
Number of labeled connected bipartite graphs on n nodes.
Number of labeled graded partially ordered sets with n elements.A001833
Number of labeled graded partially ordered sets with n elements.
a(0) = 1, a(1) = 5, a(n) = 4*a(n-1) - a(n-2).A001834
a(0) = 1, a(1) = 5, a(n) = 4*a(n-1) - a(n-2).
a(n) = 4*a(n-1) - a(n-2), with a(0) = 1, a(1) = 1.A001835
a(n) = 4*a(n-1) - a(n-2), with a(0) = 1, a(1) = 1.
Numbers k such that phi(2k-1) < phi(2k), where phi is Euler's totient function A000010.A001836
Numbers k such that phi(2k-1) < phi(2k), where phi is Euler's totient function A000010.
Numbers k such that phi(2k+1) < phi(2k).A001837
Numbers k such that phi(2k+1) < phi(2k).
Numbers k such that phi(k+2) = phi(k) + 2.A001838
Numbers k such that phi(k+2) = phi(k) + 2.
The coding-theoretic function A(n,4,3).A001839
The coding-theoretic function A(n,4,3).
Expansion of g.f. x/((1 - x)^2*(1 - x^3)).A001840
Expansion of g.f. x/((1 - x)^2*(1 - x^3)).
Related to Zarankiewicz's problem.A001841
Related to Zarankiewicz's problem.
Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).A001842
Expansion of Sum_{n>=0} x^(4*n+3)/(1 - x^(4*n+3)).
The coding-theoretic function A(n,4,4).A001843
The coding-theoretic function A(n,4,4).
Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.A001844
Centered square numbers: a(n) = 2*n*(n+1)+1. Sums of two consecutive squares. Also, consider all Pythagorean triples (X, Y, Z=Y+1) ordered by increasing Z; then sequence gives Z values.
Centered octahedral numbers (crystal ball sequence for cubic lattice).A001845
Centered octahedral numbers (crystal ball sequence for cubic lattice).
Centered 4-dimensional orthoplex numbers (crystal ball sequence for 4-dimensional cubic lattice).A001846
Centered 4-dimensional orthoplex numbers (crystal ball sequence for 4-dimensional cubic lattice).
Crystal ball sequence for 5-dimensional cubic lattice.A001847
Crystal ball sequence for 5-dimensional cubic lattice.
Crystal ball sequence for 6-dimensional cubic lattice.A001848
Crystal ball sequence for 6-dimensional cubic lattice.
Crystal ball sequence for 7-dimensional cubic lattice.A001849
Crystal ball sequence for 7-dimensional cubic lattice.
Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).A001850
Central Delannoy numbers: a(n) = Sum_{k=0..n} C(n,k)*C(n+k,k).
Total diameter of unlabeled trees with n nodes.A001851
Total diameter of unlabeled trees with n nodes.
Total diameter of labeled trees with n nodes.A001852
Total diameter of labeled trees with n nodes.
Total height of trees with n nodes.A001853
Total height of trees with n nodes.
Total height of all rooted trees on n labeled nodes.A001854
Total height of all rooted trees on n labeled nodes.
Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion.A001855
Sorting numbers: maximal number of comparisons for sorting n elements by binary insertion.
A self-generating sequence: every positive integer occurs as a(i)-a(j) for a unique pair i,j.A001856
A self-generating sequence: every positive integer occurs as a(i)-a(j) for a unique pair i,j.
a(1)=2, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.A001857
a(1)=2, a(2)=3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.
Number of forests of trees on n labeled nodes.A001858
Number of forests of trees on n labeled nodes.
Triangular numbers plus quarter-squares: n*(n+1)/2 + floor((n+1)^2/4) (i.e., A000217(n) + A002620(n+1)).A001859
Triangular numbers plus quarter-squares: n*(n+1)/2 + floor((n+1)^2/4) (i.e., A000217(n) + A002620(n+1)).