A298598 Expansion of Product_{k>=2} (1 + x^k)^k.

1, 0, 2, 3, 5, 11, 17, 32, 51, 91, 144, 241, 386, 618, 981, 1540, 2400, 3711, 5710, 8699, 13217, 19917, 29891, 44593, 66244, 97888, 144072, 211097, 308061, 447833, 648578, 935941, 1345985, 1929291, 2756440, 3926259, 5575720, 7895519, 11149261, 15701660, 22054901, 30900798, 43188113

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2018

Keywords

• nonn

Comments

Number of partitions of n into distinct parts > 1, where n different parts of size n (beginning at 2) are available (2a, 2b, 3a, 3b, 3c, 4a, 4b, 4c, 4d, ...).

Convolution of the sequences A026007 and A033999.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• Index entries for related partition-counting sequences

Crossrefs

Cf. A025147, A026007, A191659.

Programs

Mathematica

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

Formula

G.f.: Product_{k>=2} (1 + x^k)^k.

From Vaclav Kotesovec, Apr 08 2018: (Start)

a(n) + a(n+1) = A026007(n+1).

a(n) ~ Zeta(3)^(1/6) * exp((3/2)^(4/3) * Zeta(3)^(1/3) * n^(2/3)) / (2^(7/4) * 3^(1/3) * sqrt(Pi) * n^(2/3)). (End)