A357962 Expansion of e.g.f. exp( (exp(x^2) - 1)/x ).

1, 1, 1, 4, 13, 51, 271, 1366, 8849, 58717, 432541, 3530176, 29787781, 279974839, 2715912291, 28415168146, 312503079841, 3600714035321, 43979791574809, 556150585730140, 7417561518005341, 102438949373356891, 1476634705941320311, 22102618328057267694

Offset

0,4

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A357964, A357965.

Cf. A121452, A357966.

Sequence in context: A151488 A245156 A223899 * A097169 A149463 A323791

Adjacent sequences: A357959 A357960 A357961 * A357963 A357964 A357965

Keyword

nonn

Author

_Seiichi Manyama_, Oct 22 2022

Status

approved