A375588 - OEIS

A375588

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

1, 0, 0, 6, 0, 60, 720, 840, 40320, 378000, 2116800, 60207840, 598752000, 7792424640, 181863601920, 2288689603200, 45855781171200, 1016682053587200, 17113328962329600, 422970486434496000, 9765438564930048000, 213305542403822668800, 5916931500898517299200

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

LINKS

Table of n, a(n) for n=0..22.

FORMULA

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

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

CROSSREFS

Cf. A052848, A375589.