A304631 Expansion of (1/(1 - x))*Product_{k>=1} (1 + x^(2*k-1)).

1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 13, 15, 18, 21, 24, 28, 33, 38, 43, 49, 56, 64, 72, 81, 92, 104, 116, 130, 146, 163, 181, 201, 224, 249, 275, 304, 337, 372, 409, 450, 496, 545, 597, 654, 717, 785, 857, 935, 1022, 1115, 1213, 1320, 1437, 1562, 1695, 1839, 1996, 2164, 2342, 2534

Offset: 0

Author

Ilya Gutkovskiy, May 15 2018

Keywords

• nonn

Comments

Partial sums of A000700.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
• Eric Weisstein's World of Mathematics, Self-Conjugate Partition
• Index entries for sequences related to partitions

Crossrefs

Cf. A000070, A000700, A036469, A218906, A304632.

Programs

Mathematica

nmax = 59; CoefficientList[Series[1/(1 - x) Product[(1 + x^(2 k - 1)), {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 59; CoefficientList[Series[1/(1 - x) Product[1/(1 + (-x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

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

a(n) ~ exp(Pi*sqrt(n/6)) * 3^(1/4) / (Pi * 2^(1/4) * n^(1/4)). - Vaclav Kotesovec, May 19 2018