A327049 Expansion of Product_{k>=1} (1 + x^k) * (1 + x^(2*k)) * (1 + x^(3*k)) * (1 + x^(4*k)) / ((1 - x^k) * (1 - x^(2*k)) * (1 - x^(3*k)) * (1 - x^(4*k))).

1, 2, 6, 14, 32, 64, 132, 248, 466, 838, 1488, 2560, 4370, 7272, 11988, 19424, 31160, 49280, 77294, 119780, 184164, 280408, 423808, 635136, 945628, 1397398, 2052536, 2995210, 4346416, 6270272, 8999668, 12848584, 18257122, 25817760, 36349600, 50952064, 71131448

Offset

0,2

Comments

Convolution of A327046 and A327043.

Links

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

Formula

a(n) ~ 5^(5/2) * exp(5*Pi*sqrt(n/3)/2) / (2^(17/2)*3^(3/4)*n^(7/4)).

Mathematica

nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+x^(2*k)) * (1+x^(3*k)) * (1+x^(4*k))/((1-x^k) * (1-x^(2*k)) * (1-x^(3*k)) * (1-x^(4*k))), {k, 1, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A015128, A246584, A327048, A327050.

Cf. A301554.

Sequence in context: A002524 A188493 A055292 * A035592 A327050 A301554

Adjacent sequences: A327046 A327047 A327048 * A327050 A327051 A327052

Keyword

nonn

Author

Vaclav Kotesovec, Aug 16 2019

Status

approved