A319671 a(n) = [x^n] Product_{k>=2} (1 + x^k)^n.

1, 0, 2, 3, 10, 30, 77, 252, 682, 2145, 6182, 18887, 56317, 170534, 515930, 1563843, 4759338, 14480073, 44203595, 134972504, 412984510, 1264601502, 3877302717, 11898761051, 36548512477, 112358685555, 345673541514, 1064250223230, 3278695047218, 10107173174013, 31174889414807

Offset: 0

Author

Ilya Gutkovskiy, Sep 25 2018

Keywords

• nonn

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

Crossrefs

Cf. A000593, A025147, A270913, A298598, A304626, A319670.

Programs

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}]

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