A280264 G.f.: Product_{k>=1} (1+x^k) / (1+x^(k^3)).

1, 0, 1, 1, 1, 2, 2, 3, 2, 5, 4, 6, 7, 8, 10, 12, 15, 16, 21, 23, 28, 33, 38, 44, 51, 60, 68, 79, 91, 103, 120, 136, 156, 177, 202, 230, 260, 296, 333, 378, 425, 480, 540, 606, 682, 764, 857, 958, 1073, 1197, 1337, 1492, 1660, 1849, 2057, 2285, 2537, 2816

Offset: 0

Author

Vaclav Kotesovec, Dec 30 2016

Keywords

• nonn

Comments

Number of partitions of n into distinct noncubes (A007412). - Ilya Gutkovskiy, Dec 31 2016

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000009, A279329, A087154.

Programs

Mathematica

nmax=100; CoefficientList[Series[Product[(1+x^k)/(1+x^(k^3)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(Pi*sqrt(n/3) - (2^(1/3) - 1) * Gamma(1/3) * Zeta(4/3) * n^(1/6) / (3^(5/6) * Pi^(1/3))) / (2^(3/2) * 3^(1/4) * n^(3/4)).