A266650 Expansion of Product_{k>=1} (1 + x^k - x^(3*k)) / (1 - x^k).

1, 2, 4, 7, 13, 21, 34, 53, 82, 123, 181, 263, 379, 537, 754, 1047, 1444, 1972, 2675, 3601, 4820, 6408, 8473, 11141, 14580, 18985, 24611, 31765, 40839, 52294, 66719, 84819, 107474, 135731, 170892, 214518, 268524, 335190, 417308, 518212, 641948, 793324, 978157

Offset: 0

Author

Vaclav Kotesovec, Jan 02 2016

Keywords

• nonn

Comments

Convolution of A266686 and A000041.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000726, A100405, A266647, A266648, A266649, A266686.

Programs

Mathematica

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

Formula

a(n) ~ sqrt(6*c + Pi^2) * exp(sqrt((4*c + 2*Pi^2/3)*n)) / (4*sqrt(3)*Pi*n), where c = Integral_{0..infinity} log(1 + exp(-x) - exp(-3*x)) dx = 0.59698046904738615106237970379036510874974380079287087827737... . - Vaclav Kotesovec, Jan 05 2016