OFFSET
0,2
COMMENTS
Conjecture: In general, if m > 1 and a(n) = [x^n] Product_{k>=1} (1 + m^n * x^k), then log(a(n)) ~ log(m)*(sqrt(2)*n^(3/2) - n/2).
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..135
FORMULA
Conjecture: log(a(n)) ~ log(3)*sqrt(2)*n^(3/2).
MATHEMATICA
nmax = 20; Table[SeriesCoefficient[Product[(1+3^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 22 2018
STATUS
approved