OFFSET
0,3
REFERENCES
D. M. Bressoud, Analytic and combinatorial generalizations of the Rogers-Ramanujan identities, Mem. Amer. Math. Soc. 24 (1980), no. 227, 54 pp.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..5000
Andrew Sills, Rademacher-Type Formulas for Restricted Partition and Overpartition Functions, Ramanujan Journal, 23 (1-3): 253-264, 2010.
Wikipedia, Bailey pair.
FORMULA
a(n) ~ 2*Pi * BesselI(1, Pi/6 * sqrt(11*(24*n-1)/14)) / (7*sqrt((24*n-1)/11)).
a(n) ~ exp(Pi * sqrt(11*n/21)) * 11^(1/4) / (2 * 3^(1/4) * 7^(3/4) * n^(3/4)) * (1 -(3*sqrt(21)/(8*Pi*sqrt(11)) + Pi*sqrt(11)/(48*sqrt(21)))/sqrt(n) + (11*Pi^2/96768 - 315/(1408*Pi^2) + 5/128)/n).
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1-x^(7*(2*k-1))) * (1-x^(7*k)) / (1-x^k), {k, 1, nmax}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jan 11 2017
STATUS
approved