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%I #20 May 09 2022 08:38:21
%S 1,0,0,0,1,10,85,735,6839,69804,784580,9680000,130312336,1901581968,
%T 29895585356,503657235900,9051009737834,172807817059664,
%U 3493189152511608,74530548004474584,1673793045085649146,39467836062718058100,974939402596817961050,25177327470510057799550
%N Expansion of e.g.f. 1 / (1 - log(1 - x)^4 / 4!).
%H Seiichi Manyama, <a href="/A346923/b346923.txt">Table of n, a(n) for n = 0..441</a>
%F a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * |Stirling1(k,4)| * a(n-k).
%F a(n) ~ n! * 2^(-5/4) * 3^(1/4) / (exp(2^(3/4)*3^(1/4)) * (1 - exp(-2^(3/4)*3^(1/4)))^(n+1)). - _Vaclav Kotesovec_, Aug 08 2021
%F a(n) = Sum_{k=0..floor(n/4)} (4*k)! * |Stirling1(n,4*k)|/24^k. - _Seiichi Manyama_, May 06 2022
%t nmax = 23; CoefficientList[Series[1/(1 - Log[1 - x]^4/4!), {x, 0, nmax}], x] Range[0, nmax]!
%t a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Abs[StirlingS1[k, 4]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 23}]
%o (PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(1-log(1-x)^4/4!))) \\ _Michel Marcus_, Aug 07 2021
%o (PARI) a(n) = sum(k=0, n\4, (4*k)!*abs(stirling(n, 4*k, 1))/24^k); \\ _Seiichi Manyama_, May 06 2022
%Y Cf. A007840, A346921, A346922, A346924.
%Y Cf. A000454, A346895, A347003, A353119.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Aug 07 2021
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