A354550 Expansion of e.g.f. exp( x * exp(x^2/2) ).

1, 1, 1, 4, 13, 46, 241, 1156, 6889, 44668, 300241, 2328976, 18390901, 159273544, 1461200833, 13995753136, 144068872081, 1531949061136, 17259159775969, 202543867724608, 2474236899786781, 31633380519660256, 417760492214548561, 5751414293905728064

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..518

Crossrefs

Cf. A000248, A354551, A354552.

Cf. A216688.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x Exp[x^2/2]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 03 2024 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^2/2)))))

PARI

a(n) = n!*sum(k=0, n\2, (n-2*k)^k/(2^k*k!*(n-2*k)!));

Formula

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