A261629 Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^2.

1, 2, 3, 4, 5, 8, 11, 14, 17, 22, 30, 38, 46, 56, 70, 88, 106, 126, 153, 186, 224, 264, 312, 372, 440, 516, 603, 708, 830, 964, 1117, 1296, 1503, 1734, 1992, 2292, 2638, 3024, 3453, 3942, 4504, 5134, 5831, 6616, 7511, 8518, 9631, 10872, 12274, 13848, 15592

Offset

0,2

Links

Table of n, a(n) for n=0..50.

Formula

a(n) ~ exp(Pi*sqrt(n/3)) * Gamma(1/4)^2 / (8 * Pi^(3/2) * sqrt(n)).

Mathematica

nmax=60; CoefficientList[Series[Product[1/(1-x^(4*k+1))^2, {k, 0, nmax}], {x, 0, nmax}], x]

Crossrefs

Cf. A035451, A261632, A261636.

Sequence in context: A309679 A207890 A008825 * A244395 A271488 A333347

Adjacent sequences: A261626 A261627 A261628 * A261630 A261631 A261632

Keyword

nonn

Author

Vaclav Kotesovec, Aug 27 2015

Status

approved