A261651 Expansion of Product_{k>=0} ((1+x^(3*k+1))/(1-x^(3*k+1)))^3.

1, 6, 18, 38, 72, 138, 254, 432, 708, 1154, 1836, 2826, 4288, 6456, 9552, 13902, 20070, 28722, 40614, 56916, 79242, 109448, 149988, 204318, 276672, 372288, 498264, 663602, 879252, 1159470, 1522564, 1990788, 2592162, 3362638, 4346244, 5597100, 7183792, 9191004

Offset

0,2

Links

Table of n, a(n) for n=0..37.

Formula

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

Mathematica

nmax=60; CoefficientList[Series[Product[((1+x^(3*k+1))/(1-x^(3*k+1)))^3, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A015128, A156616, A080054, A007096, A261610, A261649.

Sequence in context: A270335 A270940 A270081 * A270215 A129863 A272014

Adjacent sequences: A261648 A261649 A261650 * A261652 A261653 A261654

Keyword

nonn

Author

Vaclav Kotesovec, Aug 28 2015

Status

approved