A357964 Expansion of e.g.f. exp( (exp(x^3) - 1)/x^2 ).

1, 1, 1, 1, 13, 61, 181, 1261, 12601, 77113, 481321, 6102361, 63041221, 492260341, 6041807773, 87670198981, 945716793841, 11365316711281, 193962371184721, 2824572189001393, 36983289122143741, 658584258052917421, 12073641790111934341, 185876257572349699741

Offset

0,5

Links

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

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} Stirling2(n-2*k,n-3*k)/(n-2*k)!.

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp((exp(x^3)-1)/x^2)))
(PARI) a(n) = n!*sum(k=0, n\3, stirling(n-2*k, n-3*k, 2)/(n-2*k)!);

Crossrefs

Cf. A357962, A357965.

Cf. A353223.

Sequence in context: A127876 A361657 A308461 * A353223 A302560 A252970

Adjacent sequences: A357961 A357962 A357963 * A357965 A357966 A357967

Keyword

nonn

Author

Seiichi Manyama, Oct 22 2022

Status

approved