A341714 Coefficients in the expansion of Product_{m>=1} (1 - q^(13*m))/(1 - q^m).

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 100, 134, 174, 228, 292, 378, 479, 612, 770, 972, 1213, 1519, 1881, 2334, 2874, 3540, 4331, 5302, 6450, 7848, 9501, 11496, 13851, 16680, 20006, 23980, 28648, 34193, 40689, 48378, 57360, 67948, 80295, 94788, 111652, 131388, 154293

Offset: 0

Author

N. J. A. Sloane, Feb 21 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• J. J. Webb, Arithmetic of the 13-regular partition function modulo 3, Ramanujan Journal, 25 (2011), 49-56.

Crossrefs

Column k=13 of A286653.

Formula

a(n) ~ exp(Pi*sqrt(2*n*(s-1)/(3*s))) * (s-1)^(1/4) / (2 * 6^(1/4) * s^(3/4) * n^(3/4)) * (1 + ((s-1)^(3/2)*Pi/(24*sqrt(6*s)) - 3*sqrt(6*s) / (16*Pi * sqrt(s-1))) / sqrt(n) + ((s-1)^3*Pi^2/(6912*s) - 45*s/(256*(s-1)*Pi^2) - 5*(s-1)/128) / n), set s=13. - Vaclav Kotesovec, Aug 01 2022