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A355507 Expansion of e.g.f. (1 - x)^(-x^4/24).

%I A355507 #28 Jul 21 2022 02:09:39
%S A355507 1,0,0,0,0,5,15,70,420,3024,28350,272250,2875950,33333300,420840420,
%T A355507 5763671550,84799915200,1334007397800,22343877115560,396971840865600,
%U A355507 7456250728017000,147612122975772000,3071792315894841000,67030983483724953000,1530448652869851191400
%N A355507 Expansion of e.g.f. (1 - x)^(-x^4/24).
%F A355507 a(0) = 1; a(n) = (n-1)!/24 * Sum_{k=5..n} k/(k-4) * a(n-k)/(n-k)!.
%F A355507 a(n) = n! * Sum_{k=0..floor(n/5)} |Stirling1(n-4*k,k)|/(24^k * (n-4*k)!).
%F A355507 a(n) ~ n! / (Gamma(1/24) * n^(23/24)). - _Vaclav Kotesovec_, Jul 21 2022
%o A355507 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^4/24)))
%o A355507 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^4/24*log(1-x))))
%o A355507 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/24*sum(j=5, i, j/(j-4)*v[i-j+1]/(i-j)!)); v;
%o A355507 (PARI) a(n) = n!*sum(k=0, n\5, abs(stirling(n-4*k, k, 1))/(24^k*(n-4*k)!));
%Y A355507 Column k=4 of A355610.
%Y A355507 Cf. A351493.
%K A355507 nonn
%O A355507 0,6
%A A355507 _Seiichi Manyama_, Jul 09 2022