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Expansion of e.g.f. exp(x^5 * exp(-x)).
2

%I #16 Jul 10 2022 09:41:28

%S 1,0,0,0,0,120,-720,2520,-6720,15120,1784160,-39861360,478906560,

%T -4151192760,29059190160,43589505960,-9531493695360,262248906060960,

%U -4781455284432960,68339552332044960,-719390244156842880,105128808579670680,293382376643359246320

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

%H Seiichi Manyama, <a href="/A292970/b292970.txt">Table of n, a(n) for n = 0..481</a>

%F a(n) = n! * Sum_{k=0..floor(n/5)} (-k)^(n-5*k)/(k! * (n-5*k)!). - _Seiichi Manyama_, Jul 10 2022

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

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

%o (PARI) a(n) = n!*sum(k=0, n\5, (-k)^(n-5*k)/(k!*(n-5*k)!)); \\ _Seiichi Manyama_, Jul 10 2022

%Y Column k=5 of A292973.

%K sign

%O 0,6

%A _Seiichi Manyama_, Sep 27 2017