A303902 Expansion of (1 - x^2)*Product_{k>=2} (1 + x^k)^k.

1, 0, 1, 3, 3, 8, 12, 21, 34, 59, 93, 150, 242, 377, 595, 922, 1419, 2171, 3310, 4988, 7507, 11218, 16674, 24676, 36353, 53295, 77828, 113209, 163989, 236736, 340517, 488108, 697407, 993350, 1410455, 1996968, 2819280, 3969260, 5573541, 7806141, 10905640, 15199138, 21133212

Offset: 0

Author

Ilya Gutkovskiy, May 02 2018

Keywords

• nonn

Comments

First differences of A026007.

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A002865, A026007, A087897, A191659, A298598, A302832.

Programs

Mathematica

nmax = 42; CoefficientList[Series[(1 - x^2) Product[(1 + x^k)^k, {k, 2, nmax}], {x, 0, nmax}], x]
nmax = 42; CoefficientList[Series[(1 - x) Exp[Sum[(-1)^(k + 1) x^k/(k (1 - x^k)^2), {k, 1, nmax}]], {x, 0, nmax}], x]

Formula

G.f.: (1 - x)*exp(Sum_{k>=1} (-1)^(k+1)*x^k/(k*(1 - x^k)^2)).

a(n) ~ exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(4/3)) * Zeta(3)^(1/2) / (2^(13/12) * sqrt(Pi) * n). - Vaclav Kotesovec, May 04 2018