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Euler transform of powers of 10.
3

%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