A280661 G.f.: Product_{k>=1, j>=1} 1/(1 - x^(j*k^3)).

1, 1, 2, 3, 5, 7, 11, 15, 23, 31, 44, 59, 82, 108, 146, 191, 255, 329, 431, 552, 714, 907, 1159, 1461, 1853, 2318, 2911, 3622, 4515, 5582, 6912, 8499, 10464, 12801, 15667, 19079, 23236, 28168, 34142, 41222, 49755, 59836, 71926, 86190, 103218, 123262, 147091

Offset: 0

Author

Vaclav Kotesovec, Jan 07 2017

Keywords

• nonn

Links

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

Crossrefs

Cf. A006171, A004101, A280662.

Programs

Mathematica

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

Formula

a(n) ~ exp(Pi*sqrt(2*Zeta(3)*n/3) + Pi^(-1/3) * Gamma(4/3) * Zeta(4/3) * Zeta(1/3) * (6*n/Zeta(3))^(1/6)) * Pi^(3/4) * Zeta(3)^(1/8) / (6^(1/8) * n^(5/8)).