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A341714
Coefficients in the expansion of Product_{m>=1} (1 - q^(13*m))/(1 - q^m).
4
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
0,3
LINKS
J. J. Webb, Arithmetic of the 13-regular partition function modulo 3, Ramanujan Journal, 25 (2011), 49-56.
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
CROSSREFS
Column k=13 of A286653.
Sequence in context: A218512 A008635 A008641 * A332746 A242698 A364793
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 21 2021
STATUS
approved