A279225 Expansion of Product_{k>=1} 1/(1 - x^(k^2))^2.

1, 2, 3, 4, 7, 10, 13, 16, 22, 30, 38, 46, 58, 74, 90, 106, 129, 158, 190, 222, 264, 314, 370, 426, 495, 580, 674, 772, 886, 1024, 1174, 1332, 1512, 1724, 1961, 2210, 2494, 2818, 3180, 3558, 3984, 4468, 5003, 5572, 6202, 6918, 7698, 8530, 9440, 10466, 11589

Offset: 0

Author

Vaclav Kotesovec, Dec 08 2016

Keywords

• nonn

Comments

Number of partitions of n into squares of 2 kinds. - Ilya Gutkovskiy, Jan 23 2018

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001156, A103265, A279226, A279227.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - x^(k^2))^2, {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp(3 * Pi^(1/3) * Zeta(3/2)^(2/3) * n^(1/3) / 2^(2/3)) * Zeta(3/2) / (8 * sqrt(3) * Pi^2 * n^(3/2)). - Vaclav Kotesovec, Dec 29 2016