A292837 Euler transform of powers of 10.

1, 10, 155, 2220, 31265, 429502, 5796455, 77009640, 1009734835, 13088591470, 167965714273, 2136403822060, 26958029557805, 337733366170870, 4203655872002815, 52010628718162744, 639999271669543500, 7835602953248681200, 95484165081421513000

Offset: 0

Author

Alois P. Heinz, Sep 24 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..975

Crossrefs

Column k=10 of A144074.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, add(add(d*
      10^d, d=numtheory[divisors](j))*a(n-j), j=1..n)/n)
    end:
seq(a(n), n=0..30);

Formula

G.f.: Product_{j>0} 1/(1-x^j)^(10^j).

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

G.f.: exp(10*Sum_{k>=1} x^k/(k*(1 - 10*x^k))). - Ilya Gutkovskiy, Nov 10 2018