A261647 Expansion of Product_{k>=0} ((1+x^(2*k+1))/(1-x^(2*k+1)))^3.

1, 6, 18, 44, 102, 216, 428, 816, 1494, 2650, 4584, 7740, 12804, 20808, 33264, 52400, 81462, 125100, 189966, 285516, 425016, 627040, 917436, 1331856, 1919332, 2746926, 3905784, 5519352, 7754064, 10833192, 15055216, 20817600, 28647414, 39241336, 53517060

Offset: 0

Author

Vaclav Kotesovec, Aug 28 2015

Keywords

• nonn

Links

• Vaclav Kotesovec, A method of finding the asymptotics of q-series based on the convolution of generating functions, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 11.

Crossrefs

Cf. A015128, A156616.

Cf. A080054, A007096, A014969, A261648, A014970, A014972, A103261.

Cf. A261610, A261649, A261651.

Cf. A261611, A261650, A261652.

Programs

Mathematica

nmax=60; CoefficientList[Series[Product[((1+x^(2*k+1))/(1-x^(2*k+1)))^3,{k,0,nmax}],{x,0,nmax}],x]

Formula

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