A261610 Expansion of Product_{k>=0} (1 + x^(3*k+1))/(1 - x^(3*k+1)).

1, 2, 2, 2, 4, 6, 6, 8, 12, 14, 16, 22, 28, 32, 40, 50, 58, 70, 86, 100, 118, 144, 168, 194, 232, 272, 312, 366, 428, 490, 568, 660, 754, 866, 1000, 1140, 1300, 1492, 1696, 1924, 2196, 2490, 2812, 3192, 3610, 4062, 4588, 5174, 5806, 6530, 7342, 8218, 9208

Offset

0,2

Links

Table of n, a(n) for n=0..52.

Formula

a(n) ~ exp(Pi*sqrt(n/3)) * Gamma(1/3) / (2^(5/3) * 3^(1/3) * Pi^(2/3) * n^(2/3)).

Mathematica

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

Crossrefs

Cf. A015128, A080054, A261611.

Sequence in context: A365719 A096575 A002722 * A265251 A336032 A093393

Adjacent sequences: A261607 A261608 A261609 * A261611 A261612 A261613

Keyword

nonn

Author

Vaclav Kotesovec, Aug 26 2015

Status

approved