A357967 Expansion of e.g.f. exp( x * (exp(x^3) - 1) ).

1, 0, 0, 0, 24, 0, 0, 2520, 20160, 0, 604800, 19958400, 79833600, 259459200, 25427001600, 326918592000, 1046139494400, 44460928512000, 1333827855360000, 10306043229081600, 125024130975744000, 6386367771463680000, 101695303941783552000, 861733891296165888000

Offset

0,5

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A357966, A357968.

Cf. A353227.

Sequence in context: A267334 A202184 A368027 * A353227 A375589 A375562

Adjacent sequences: A357964 A357965 A357966 * A357968 A357969 A357970

Keyword

nonn

Author

Seiichi Manyama, Oct 22 2022

Status

approved