A327045 Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)).

1, 1, 2, 4, 5, 8, 13, 17, 24, 36, 47, 64, 89, 115, 152, 204, 260, 336, 438, 552, 702, 896, 1117, 1400, 1758, 2171, 2688, 3332, 4079, 5000, 6131, 7446, 9048, 10992, 13255, 15984, 19264, 23081, 27644, 33084, 39408, 46912, 55797, 66107, 78264, 92572, 109140

Offset: 0

Author

Vaclav Kotesovec, Aug 16 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000009, A001935, A327046, A327047.

Cf. A107742, A327042.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(2*k)) * (1+x^(3*k)), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ 11^(1/4) * exp(sqrt(11*n/2)*Pi/3) / (2^(13/4)*sqrt(3)*n^(3/4)).