A144073 Euler transform of powers of 9.

1, 9, 126, 1623, 20583, 254493, 3091803, 36974025, 436377771, 5091463423, 58811218362, 673298882775, 7647050353038, 86229872235432, 966019964324004, 10757807941399023, 119146632352548516, 1312935665205028374, 14400230629085596621, 157253909597473608945

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

G.f.: Product_{j>0} 1/(1-x^j)^(9^j).

a(n) ~ 9^n * exp(2*sqrt(n) - 1/2 + c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} 1/(m*(9^(m-1)-1)) = 0.0670436814415340801450018457068097893307906... . - Vaclav Kotesovec, Mar 14 2015

G.f.: exp(9*Sum_{k>=1} x^k/(k*(1 - 9*x^k))). - Ilya Gutkovskiy, Nov 10 2018

Maple

with(numtheory): etr:= proc(p) local b; b:=proc(n) option remember; `if`(n=0, 1, add(add(d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n) end end: a:=n-> etr(j->9^j)(n): seq(a(n), n=0..40);

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1-x^j)^(9^j), {j, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)

Crossrefs

9th column of A144074.

Cf. A001019 (powers of 9).

Sequence in context: A261176 A261743 A229283 * A261801 A065086 A246238

Adjacent sequences: A144070 A144071 A144072 * A144074 A144075 A144076

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2008

Status

approved