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

Author

Seiichi Manyama, Oct 22 2022

Keywords

• nonn

Crossrefs

Cf. A357964, A357965.

Cf. A121452, A357966.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[(Exp[x^2]-1)/x],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 19 2024 *)

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)!);

Formula

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