login
A058507
McKay-Thompson series of class 14c for Monster.
1
1, 5, 13, 37, 71, 142, 250, 457, 750, 1263, 2035, 3229, 4988, 7649, 11488, 17092, 25081, 36531, 52491, 74950, 105860, 148675, 206914, 286401, 393536, 537848, 730398, 987086, 1326645, 1774901, 2363069, 3133327, 4135942, 5438861, 7123396, 9297096, 12089350, 15669436
OFFSET
-1,2
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
Expansion of A +7*q/A, where A = q^(1/2)*(eta(q)/eta(q^7))^2, in powers of q. - G. C. Greubel, Jun 20 2018
a(n) ~ exp(2*Pi*sqrt(2*n/7)) / (2^(3/4) * 7^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018
EXAMPLE
T14c = 1/q + 5*q + 13*q^3 + 37*q^5 + 71*q^7 + 142*q^9 + 250*q^11 + ...
MATHEMATICA
QP = QPochhammer; A = (QP[q]/QP[q^7])^2 + O[q]^50; CoefficientList[A + 7*q/A, q] (* Georg Fischer, Nov 14 2020 *)
PROG
(PARI) q='q+O('q^50); A= (eta(q)/eta(q^7))^2; Vec(A +7*q/A) \\ G. C. Greubel, Jun 20 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 20 2018
STATUS
approved