A292970 Expansion of e.g.f. exp(x^5 * exp(-x)).

1, 0, 0, 0, 0, 120, -720, 2520, -6720, 15120, 1784160, -39861360, 478906560, -4151192760, 29059190160, 43589505960, -9531493695360, 262248906060960, -4781455284432960, 68339552332044960, -719390244156842880, 105128808579670680, 293382376643359246320

Offset: 0

Author

Seiichi Manyama, Sep 27 2017

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..481

Crossrefs

Column k=5 of A292973.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x^5 Exp[-x]],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 12 2018 *)

PARI

x='x+O('x^66); Vec(serlaplace(exp(x^5*exp(-x))))

PARI

a(n) = n!*sum(k=0, n\5, (-k)^(n-5*k)/(k!*(n-5*k)!)); \\ Seiichi Manyama, Jul 10 2022

Formula

a(n) = n! * Sum_{k=0..floor(n/5)} (-k)^(n-5*k)/(k! * (n-5*k)!). - Seiichi Manyama, Jul 10 2022