A327048 Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)) / ((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k))).

1, 2, 6, 14, 30, 60, 120, 220, 402, 710, 1224, 2064, 3438, 5596, 9012, 14304, 22422, 34740, 53330, 80960, 121908, 181976, 269484, 396072, 578232, 838258, 1207896, 1730058, 2463900, 3490020, 4918572, 6897012, 9626610, 13375776, 18504852, 25494456, 34985530

Offset: 0

Author

Vaclav Kotesovec, Aug 16 2019

Keywords

• nonn

Comments

Convolution of A327045 and A327042.

Links

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

Crossrefs

Cf. A015128, A246584, A327049, A327050.

Cf. A301554.

Programs

Mathematica

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

Formula

a(n) ~ 11 * exp(sqrt(11*n/6)*Pi) / (2^(13/2)*sqrt(3)*n^(3/2)).