A261631 Expansion of Product_{k>=0} 1/(1-x^(3*k+1))^3.

1, 3, 6, 10, 18, 30, 46, 69, 105, 154, 219, 309, 434, 597, 813, 1100, 1476, 1959, 2585, 3387, 4410, 5709, 7353, 9414, 12001, 15231, 19242, 24205, 30348, 37902, 47165, 58500, 72342, 89169, 109599, 134337, 164221, 200226, 243537, 295496, 357732, 432117, 520858

Offset: 0

Author

Vaclav Kotesovec, Aug 27 2015

Keywords

• nonn

Crossrefs

Cf. A035382, A261616, A261632.

Programs

Mathematica

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

Formula

a(n) ~ exp(Pi*sqrt(2*n/3)) * Gamma(1/3)^3 / (4 * Pi^2 * sqrt(6*n)).