A353894 Expansion of e.g.f. exp( (x * (exp(x) - 1))^2 / 4 ).

1, 0, 0, 0, 6, 30, 105, 315, 2128, 24948, 251415, 2093025, 16437036, 148728294, 1693067467, 21459867975, 270217289280, 3338860150488, 42428729660751, 581966068060485, 8654787480759700, 135253842794286930, 2163416823356628147, 35313421249845594075

Offset

0,5

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((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*k!*(n-2*k)!));

Crossrefs

Cf. A052506, A353895, A353896.

Cf. A060311, A353883, A353891.

Sequence in context: A074007 A152573 A348257 * A353883 A258723 A225382

Adjacent sequences: A353891 A353892 A353893 * A353895 A353896 A353897

Keyword

nonn

Author

Seiichi Manyama, May 09 2022

Status

approved