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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 09 2008
STATUS
approved