OFFSET
0,9
COMMENTS
In general, if m > 1 and g.f. = Product_{k>=1} (1 + x^(m*k))/(1 + x^k), then a(n) ~ (-1)^n * exp(Pi*sqrt((m+2)*n/(6*m))) * (m+2)^(1/4) / (4 * (6*m)^(1/4) * n^(3/4)) if m is even and a(n) ~ (-1)^n * exp(Pi*sqrt((m-1)*n/(6*m))) * (m-1)^(1/4) / (2^(3/2) * (6*m)^(1/4) * n^(3/4)) if m is odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) ~ (-1)^n * exp(2*Pi*sqrt(n/3)/3) / (2 * 3^(3/4) * n^(3/4)).
MAPLE
with(numtheory):
a:= proc(n) option remember; `if`(n=0, 1, add(add(d*[0, -1, 0,
-1, 0, -1, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -1]
[1+irem(d, 18)], d=divisors(j))*a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..80); # Alois P. Heinz, Sep 01 2015
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1 + x^(9*k))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
sign
AUTHOR
Vaclav Kotesovec, Aug 30 2015
STATUS
approved