A292891 Expansion of e.g.f. exp(x^3 * (exp(x) - 1)).

1, 0, 0, 0, 24, 60, 120, 210, 20496, 181944, 1059120, 4990590, 100458600, 1634594676, 18436740504, 164378216730, 2124284725920, 38171412643440, 631390188466656, 8760417873485814, 124649582165430840, 2167585391936047020, 41833303600025220360

Offset

0,5

Links

Seiichi Manyama, Table of n, a(n) for n = 0..200

Formula

From Seiichi Manyama, Jul 09 2022: (Start)

a(n) = n! * Sum_{k=0..floor(n/4)} Stirling2(n-3*k,k)/(n-3*k)!.

a(0) = 1; a(n) = (n-1)! * Sum_{k=4..n} k/(k-3)! * a(n-k)/(n-k)!. (End)

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x^3 (Exp[x]-1)], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 21 2022 *)

Prog

(PARI) x='x+O('x^66); Vec(serlaplace(exp(x^3*(exp(x)-1))))
(PARI) a(n) = n!*sum(k=0, n\4, stirling(n-3*k, k, 2)/(n-3*k)!); \\ Seiichi Manyama, Jul 09 2022
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=4, i, j/(j-3)!*v[i-j+1]/(i-j)!)); v; \\ Seiichi Manyama, Jul 09 2022

Crossrefs

Column k=3 of A292892.

Cf. A292889, A354001.

Sequence in context: A101860 A163636 A279930 * A366751 A358014 A356950

Adjacent sequences: A292888 A292889 A292890 * A292892 A292893 A292894

Keyword

nonn

Author

Seiichi Manyama, Sep 26 2017

Status

approved