A144072 Euler transform of powers of 8.

1, 8, 100, 1144, 12906, 141848, 1532276, 16290920, 170938483, 1773107760, 18208004664, 185316171472, 1871103319988, 18756665504080, 186798940872312, 1849265718114736, 18207140415436701, 178355043327697976, 1738966407826985884, 16881111732250394440

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)^(8^j).

a(n) ~ 8^n * exp(2*sqrt(n) - 1/2 + c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} 1/(m*(8^(m-1)-1)) = 0.0772633520042039151361539536110877247158170... . - Vaclav Kotesovec, Mar 14 2015

G.f.: exp(8*Sum_{k>=1} x^k/(k*(1 - 8*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->8^j)(n): seq(a(n), n=0..40);

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(1-x^j)^(8^j), {j, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 14 2015 *)

Crossrefs

8th column of A144074.

Cf. A001018 (powers of 8).

Sequence in context: A222486 A229282 A179485 * A261800 A208705 A246237

Adjacent sequences: A144069 A144070 A144071 * A144073 A144074 A144075

Keyword

nonn

Author

Alois P. Heinz, Sep 09 2008

Status

approved