A354551 Expansion of e.g.f. exp( x * exp(x^3/6) ).

1, 1, 1, 1, 5, 21, 61, 211, 1401, 8065, 37241, 240021, 1997821, 13856701, 94418325, 874328911, 8304303281, 69158458881, 658339599601, 7454839614985, 78224066633781, 805961931388741, 9828080719704941, 124199805022959051, 1466207770078872745

Offset: 0

Author

Seiichi Manyama, Aug 18 2022

Keywords

• nonn

Comments

This sequence is different from A143567.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..523

Crossrefs

Cf. A000248, A354550, A354552.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x*Exp[x^3/6]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 03 2025 *)

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x*(exp(x^3/6)))))

PARI

a(n) = n!*sum(k=0, n\3, (n-3*k)^k/(6^k*k!*(n-3*k)!));

Formula

a(n) = n! * Sum_{k=0..floor(n/3)} (n - 3*k)^k/(6^k * k! * (n - 3*k)!).