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%I #18 Jul 10 2022 09:07:01
%S 1,0,0,0,24,-120,360,-840,21840,-365904,3633840,-26619120,239512680,
%T -3943797000,69258333144,-997361197560,12707273822880,
%U -179576670930720,3215428464641760,-62865157116396384,1167555972633639480,-20756362432008412440
%N Expansion of e.g.f. exp(x^4 * exp(-x)).
%H Seiichi Manyama, <a href="/A292969/b292969.txt">Table of n, a(n) for n = 0..487</a>
%F a(n) = n! * Sum_{k=0..floor(n/4)} (-k)^(n-4*k)/(k! * (n-4*k)!). - _Seiichi Manyama_, Jul 10 2022
%p S:= series(exp(x^4*exp(-x)),x,51):
%p seq(coeff(S,x,j)*j!,j=0..50); # _Robert Israel_, Sep 28 2017
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^4*exp(-x))))
%o (PARI) a(n) = n!*sum(k=0, n\4, (-k)^(n-4*k)/(k!*(n-4*k)!)); \\ _Seiichi Manyama_, Jul 10 2022
%Y Column k=4 of A292973.
%Y Cf. A292979.
%K sign
%O 0,5
%A _Seiichi Manyama_, Sep 27 2017
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