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%I #10 Aug 23 2019 20:52:02
%S 1,5,35,190,1070,5525,29080,147485,752790,3789170,19105800,95794930,
%T 480650335,2406018490,12047084370,60264282575,301493182380,
%U 1507758356660,7540528037090,37705593514220,188545393000350,942756783659980,4713958620697385,23570092258449540
%N Expansion of Product_{k>=1} 1/(1 - 5*k*x^k).
%H Vaclav Kotesovec, <a href="/A265976/b265976.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) ~ c * 5^n, where c = Product_{m>=2} 1/(1 - m/5^(m-1)) = 1.977268427518901757865749340705853730491796767544158844539130847296...
%p b:= proc(n, i) option remember; `if`(n=0 or i=1,
%p 5^n, b(n, i-1) +i*5*b(n-i, min(n-i, i)))
%p end:
%p a:= n-> b(n$2):
%p seq(a(n), n=0..32); # _Alois P. Heinz_, Aug 23 2019
%t nmax=40; CoefficientList[Series[Product[1/(1-5*k*x^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A006906, A265951, A265974, A265975.
%Y Cf. A246935, A246937.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Dec 19 2015
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