A327050 -id:A327050 - cp's OEIS frontend

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

Vaclav Kotesovec, Aug 16 2019

nonn

Convolution of A327045 and A327042.

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

Cf. A015128, A246584, A327049, A327050.

Cf. A301554.

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]

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

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

Original entry on oeis.org

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

Vaclav Kotesovec, Aug 16 2019

nonn

Convolution of A327046 and A327043.

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

Cf. A015128, A246584, A327048, A327050.

Cf. A301554.

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]

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

cp's OEIS Frontend

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

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

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cp's OEIS Frontend

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))).

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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))).

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

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