A000222 a(n) = A058057(n,n-2). (Formerly M2602 N1029)

0, 0, 1, 3, 6, 38, 213, 1479, 11692, 104364, 1036809, 11344859, 135548466, 1755739218, 24504637741, 366596136399, 5852040379224, 99283915922264, 1783921946910417, 33840669046326579, 675849838112277598, 14174636583759324798

Offset

0,4

References

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 198.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..150

R. C. Read, Letter to N. J. A. Sloane, Oct. 29, 1976

Formula

a(n) ~ 2/exp(2) * n!. - Vaclav Kotesovec, Sep 06 2014

a(n)+2*a(n+p)+a(n+2*p) is divisible by p for any prime p. - Mark van Hoeij, Jun 13 2019

a(n) = Sum_{k=2..n} (-1)^k * (n-k)! * binomial(k,2) * binomial(2*n-k,k). - Seiichi Manyama, Jun 21 2026

Mathematica

max = 30; f[x_, y_] := Sum[n!*((x*y)^n/(1+x*(y-1))^(2*n+1)), {n, 0, max}]; t = MapIndexed[Take[#1, First[#2]]&, CoefficientList[Series[f[x, y], {x, 0, max}, {y, 0, max}], {x, y}]] ; a[0] = a[1] = 0; a[n_] := t[[n+1, n-1]]; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Mar 11 2014, after Vladeta Jovovic *)

Prog

(PARI) a(n) = sum(k=2, n, (-1)^k*(n-k)!*binomial(k, 2)*binomial(2*n-k, k)); \\ Seiichi Manyama, Jun 21 2026

Crossrefs

A diagonal of A058057.

Sequence in context: A025596 A172361 A114038 * A372017 A208649 A371063

Adjacent sequences: A000219 A000220 A000221 * A000223 A000224 A000225

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Name changed by Seiichi Manyama, Jun 21 2026

Status

approved