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

0,2

Links

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

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

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);

Crossrefs

Column k=10 of A144074.

Sequence in context: A261744 A229284 A087603 * A261802 A246239 A235340

Adjacent sequences: A292834 A292835 A292836 * A292838 A292839 A292840

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2017

Status

approved