A375665 Expansion of e.g.f. 1 / (1 - x * (exp(x^2) - 1))^3.

1, 0, 0, 18, 0, 180, 4320, 2520, 241920, 3674160, 12700800, 599749920, 7903526400, 77863705920, 2660390853120, 37269497865600, 683129089843200, 19948163057222400, 339567800885913600, 8690022866119795200, 241333983478748160000, 5217670959100125926400

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

E.g.f.: B(x)^3, where B(x) is the e.g.f. of A375588.

a(n) = (n!/2) * Sum_{k=0..floor(n/2)} (n-2*k+2)! * Stirling2(k,n-2*k)/k!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x-x*exp(x^2))^3))
(PARI) a(n) = n!*sum(k=0, n\2, (n-2*k+2)!*stirling(k, n-2*k, 2)/k!)/2;

Crossrefs

Cf. A375588, A375664.

Sequence in context: A335187 A231962 A052441 * A375681 A376444 A376442

Adjacent sequences: A375662 A375663 A375664 * A375666 A375667 A375668

Keyword

nonn

Author

Seiichi Manyama, Aug 23 2024

Status

approved