%I #10 Nov 10 2018 05:47:24
%S 1,10,155,2220,31265,429502,5796455,77009640,1009734835,13088591470,
%T 167965714273,2136403822060,26958029557805,337733366170870,
%U 4203655872002815,52010628718162744,639999271669543500,7835602953248681200,95484165081421513000
%N Euler transform of powers of 10.
%H Alois P. Heinz, <a href="/A292837/b292837.txt">Table of n, a(n) for n = 0..975</a>
%F G.f.: Product_{j>0} 1/(1-x^j)^(10^j).
%F a(n) ~ 10^n * exp(2*sqrt(n) - 1/2 + c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} 1/(m*(10^(m-1)-1)) = 0.0591946344347498235857176537123415539... - _Vaclav Kotesovec_, Sep 28 2017
%F G.f.: exp(10*Sum_{k>=1} x^k/(k*(1 - 10*x^k))). - _Ilya Gutkovskiy_, Nov 10 2018
%p a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
%p 10^d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
%p end:
%p seq(a(n), n=0..30);
%Y Column k=10 of A144074.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Sep 24 2017