A358064 Expansion of e.g.f. 1/(1 - x * exp(x^2)).

1, 1, 2, 12, 72, 540, 5040, 53760, 658560, 9087120, 139104000, 2343781440, 43078210560, 857676980160, 18390744852480, 422504399116800, 10353592759910400, 269576216304595200, 7431814422621388800, 216266552026593868800, 6624610236968435712000

Offset: 0

Author

Seiichi Manyama, Oct 29 2022

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..420

Crossrefs

Cf. A216688, A358065.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[1/(1-x Exp[x^2]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Feb 14 2024 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x*exp(x^2))))

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k)^k/k!);

Formula

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

a(n) ~ n! * 2^(n/2) / ((1 + LambertW(2)) * LambertW(2)^(n/2)). - Vaclav Kotesovec, Nov 01 2022