A107235 Expansion of 1 / Product_{n>=0} (1 - q^(5n+1))*(1 - q^(5n+2))*(1 - q^(5n+4)).

1, 1, 2, 2, 4, 4, 7, 8, 12, 14, 19, 23, 31, 37, 48, 57, 73, 86, 109, 128, 159, 187, 229, 269, 326, 382, 458, 535, 638, 742, 879, 1019, 1200, 1388, 1625, 1875, 2185, 2514, 2916, 3347, 3868, 4427, 5099, 5822, 6683, 7614, 8712, 9904, 11301, 12821, 14589

Offset: 0

Author

Ralf Stephan, May 13 2005

Keywords

• nonn

Links

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

Crossrefs

Cf. A035959, A107234, A107236, A107237.

Programs

Mathematica

nmax = 50; CoefficientList[Series[1/Product[(1 - x^(5*k+1))*(1 - x^(5*k+2))*(1 - x^(5*k+4)), {k, 0, nmax/5}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 07 2021 *)

Formula

a(n) ~ Pi^(2/5) * exp(Pi*sqrt(2*n/5)) / (Gamma(3/5) * 2^(7/10) * 5^(4/5) * n^(7/10)). - Vaclav Kotesovec, Jan 07 2021