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%I #27 Sep 07 2023 08:47:33
%S 1,1,7,86,1524,35370,1015590,34757400,1381147440,62498177880,
%T 3172764322680,178566159846480,11034757650750960,742773843654742080,
%U 54094804600076176320,4238009228531321452800,355400361455423327193600,31764402860426288679456000,3014207878695233997923193600
%N Expansion of e.g.f. 1 / (1 + 5 * log(1 - x))^(1/5).
%H Seiichi Manyama, <a href="/A346987/b346987.txt">Table of n, a(n) for n = 0..350</a>
%F a(n) = Sum_{k=0..n} |Stirling1(n,k)| * A008548(k).
%F a(n) ~ n! * exp(n/5) / (Gamma(1/5) * 5^(1/5) * n^(4/5) * (exp(1/5) - 1)^(n + 1/5)). - _Vaclav Kotesovec_, Aug 14 2021
%F For n > 0, a(n) = Sum_{k=1..n} (n!/(n-k)!)*(5/k-4/n)*a(n-k). - _Tani Akinari_, Aug 27 2023
%t nmax = 18; CoefficientList[Series[1/(1 + 5 Log[1 - x])^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[Abs[StirlingS1[n, k]] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]
%o (Maxima) a[n]:=if n=0 then 1 else sum(n!/(n-k)!*(5/k-4/n)*a[n-k],k,1,n);
%o makelist(a[n],n,0,50); /* _Tani Akinari_, Aug 27 2023 */
%Y Cf. A007840, A008548, A346978, A346984, A347015, A347016, A347019.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Aug 11 2021
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