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%I #12 Nov 19 2021 08:46:00
%S 1,6,41,356,4401,78826,1893481,56341416,1978638881,79749105326,
%T 3622010623401,182895318578956,10160561511881041,615728464210461906,
%U 40414538467581457001,2855999961062529064976,216180544920721807887681
%N E.g.f.: exp(5x)/(1-5x)^(1/5).
%C Sum_{k = 0..n} A046716(n,k)*x^k give A000522(n), A081367(n), A094822(n), A094856(n) for x = 1, 2, 3, 4 respectively.
%F a(n) = Sum_{k = 0..n} A046716(n, k)*5^k.
%F Conjectured to be D-finite with recurrence: a(n) +(-5*n-1)*a(n-1) +25*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 15 2019
%F a(n) ~ sqrt(2*Pi) * 5^n * n^(n - 3/10) / (Gamma(1/5) * exp(n-1)). - _Vaclav Kotesovec_, Nov 19 2021
%t With[{nn=20},CoefficientList[Series[Exp[5x]/(1-5x)^(1/5),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, May 19 2014 *)
%K nonn
%O 0,2
%A _Philippe Deléham_, Jun 16 2004