OFFSET
0,3
COMMENTS
Number of partitions of n into distinct parts > 1, with n types of each part.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = [x^n] exp(n*Sum_{k>=1} (A000593(k) + (-1)^k)*x^k/k).
a(n) ~ c * d^n / sqrt(n), where d = 3.136240011804974455586379053639831470878466... and c = 0.220695581251514154138820799337758703024... - Vaclav Kotesovec, Oct 06 2018
MATHEMATICA
Table[SeriesCoefficient[Product[(1 + x^k)^n, {k, 2, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[1/((1 + x) QPochhammer[x, x^2])^n, {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Exp[n Sum[(Sum[Mod[d, 2] d, {d, Divisors[k]}] + (-1)^k) x^k/k, {k, 1, n}]], {x, 0, n}], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 25 2018
STATUS
approved