A262884 Expansion of Product_{k>=1} ((1+x^(3*k-1))*(1+x^(3*k-2)))^k.

1, 1, 1, 1, 2, 4, 4, 7, 9, 11, 16, 23, 31, 40, 53, 71, 91, 121, 161, 206, 264, 343, 441, 563, 725, 922, 1166, 1476, 1869, 2357, 2967, 3725, 4659, 5816, 7263, 9050, 11241, 13947, 17269, 21333, 26342, 32479, 39957, 49094, 60231, 73775, 90273, 110333, 134643

Offset: 0

Author

Vaclav Kotesovec, Oct 04 2015

Keywords

• nonn

Comments

Convolution of A262878 and A262879.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..2000
• 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

Crossrefs

Cf. A262878, A262879, A262883, A262924.

Programs

Mathematica

nmax = 50; CoefficientList[Series[Product[((1+x^(3*k-1))*(1+x^(3*k-2)))^k, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(-Pi^4/(2592*Zeta(3)) + Pi^2 * n^(1/3) / (12*3^(2/3)*Zeta(3)^(1/3)) + 3^(2/3) * Zeta(3)^(1/3) * n^(2/3)/2) * Zeta(3)^(1/6) / (2^(7/18) * 3^(2/3) * sqrt(Pi) * n^(2/3)).