A358264 Expansion of e.g.f. 1/(1 - x * exp(x^2/2)).

1, 1, 2, 9, 48, 315, 2520, 23415, 248640, 2972025, 39463200, 576413145, 9184855680, 158550787395, 2947473809280, 58707685211175, 1247293022976000, 28156003910859825, 672972205556851200, 16978695795089253225, 450907982644863744000, 12573634144960773960075

Offset

0,3

Links

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

Formula

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

a(n) ~ n! / ((1 + LambertW(1)) * LambertW(1)^(n/2)). - Vaclav Kotesovec, Nov 13 2022

Prog

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

Crossrefs

Cf. A006153, A358265.

Cf. A354550, A358064.

Sequence in context: A205571 A354312 A052826 * A246759 A191005 A257544

Adjacent sequences: A358261 A358262 A358263 * A358265 A358266 A358267

Keyword

nonn,easy

Author

Seiichi Manyama, Nov 06 2022

Status

approved