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%I #8 Aug 14 2021 08:47:03
%S 1,2,9,88,1361,28182,726889,22414988,803913441,32867765002,
%T 1508608850249,76804271962848,4294870015118641,261673684619584862,
%U 17252970318529474089,1223896705010751194068,92946073511938131386561,7523666291578066678172562,646658551118777059833155209
%N E.g.f.: exp(x) / (1 - 5 * x)^(1/5).
%C Binomial transform of A008548.
%F a(n) = Sum_{k=0..n} binomial(n,k) * A008548(k).
%F a(n) ~ n! * exp(1/5) * 5^n / (Gamma(1/5) * n^(4/5)). - _Vaclav Kotesovec_, Aug 14 2021
%p g:= proc(n) option remember; `if`(n<2, 1, (5*n-4)*g(n-1)) end:
%p a:= n-> add(binomial(n, k)*g(k), k=0..n):
%p seq(a(n), n=0..18); # _Alois P. Heinz_, Aug 10 2021
%t nmax = 18; CoefficientList[Series[Exp[x]/(1 - 5 x)^(1/5), {x, 0, nmax}], x] Range[0, nmax]!
%t Table[Sum[Binomial[n, k] 5^k Pochhammer[1/5, k], {k, 0, n}], {n, 0, 18}]
%t Table[HypergeometricU[1/5, n + 6/5, 1/5]/5^(1/5), {n, 0, 18}]
%Y Cf. A000522, A008548, A056546, A084262, A088992, A346258, A347012, A347014.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Aug 10 2021