A353883 Expansion of e.g.f. 1/(1 - (x * (exp(x) - 1))^2 / 4).

1, 0, 0, 0, 6, 30, 105, 315, 3388, 47628, 497115, 4172025, 37829946, 491971194, 7699457857, 114432747975, 1602464966040, 23767387469688, 408590795439351, 7756561553900085, 149537297087139910, 2889288053301888630, 58297667473293537597

Offset: 0

Author

Seiichi Manyama, May 09 2022

Keywords

• nonn

Crossrefs

Cf. A052848, A353884, A353885.

Cf. A330047, A353880.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^2/4)))

PARI

a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*(n-2*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * Stirling2(n-2*k,2*k)/(4^k * (n-2*k)!).