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A354624 Expansion of e.g.f. (1 - x)^(-x^4).

%I A354624 #12 Jul 21 2022 02:04:28
%S A354624 1,0,0,0,0,120,360,1680,10080,72576,2419200,25660800,279417600,
%T A354624 3286483200,41894012160,794511244800,13755488947200,238514695372800,
%U A354624 4269265386946560,79696849513881600,1658065431859200000
%N A354624 Expansion of e.g.f. (1 - x)^(-x^4).
%F A354624 a(0) = 1; a(n) = (n-1)! * Sum_{k=5..n} k/(k-4) * a(n-k)/(n-k)!.
%F A354624 a(n) = n! * Sum_{k=0..floor(n/5)} |Stirling1(n-4*k,k)|/(n-4*k)!.
%F A354624 a(n) ~ n! * (1 - 4/n - 16*log(n)/n^2). - _Vaclav Kotesovec_, Jul 21 2022
%o A354624 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^4)))
%o A354624 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^4*log(1-x))))
%o A354624 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=5, i, j/(j-4)*v[i-j+1]/(i-j)!)); v;
%o A354624 (PARI) a(n) = n!*sum(k=0, n\5, abs(stirling(n-4*k, k, 1))/(n-4*k)!);
%Y A354624 Column k=4 of A355609.
%Y A354624 Cf. A353228, A353229.
%Y A354624 Cf. A354625.
%K A354624 nonn
%O A354624 0,6
%A A354624 _Seiichi Manyama_, Jul 09 2022