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A353358 Expansion of e.g.f. exp(log(1 - x)^4).

%I A353358 #19 Oct 19 2022 11:11:54
%S A353358 1,0,0,0,24,240,2040,17640,182616,2340576,34907520,567732000,
%T A353358 9811675104,179804319552,3507724531584,72964001073600,
%U A353358 1614757714491456,37860036000293376,936291898320463872,24333527620574701056,662723505438520771584,18871765275000834201600
%N A353358 Expansion of e.g.f. exp(log(1 - x)^4).
%H A353358 Seiichi Manyama, <a href="/A353358/b353358.txt">Table of n, a(n) for n = 0..438</a>
%F A353358 E.g.f.: (1 - x)^((log(1 - x))^3).
%F A353358 a(0) = 1; a(n) = 24 * Sum_{k=1..n} binomial(n-1,k-1) * |Stirling1(k,4)| * a(n-k).
%F A353358 a(n) = Sum_{k=0..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/k!.
%o A353358 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(log(1-x)^4)))
%o A353358 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(log(1-x)^3)))
%o A353358 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=24*sum(j=1, i, binomial(i-1, j-1)*abs(stirling(j, 4, 1))*v[i-j+1])); v;
%o A353358 (PARI) a(n) = sum(k=0, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/k!);
%Y A353358 Column k=4 of A357882.
%Y A353358 Cf. A000142, A353344, A353404.
%Y A353358 Cf. A347003, A353119, A353665.
%K A353358 nonn
%O A353358 0,5
%A A353358 _Seiichi Manyama_, May 06 2022