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A058505
McKay-Thompson series of class 14a for Monster.
1
1, -9, -15, -33, -69, -138, -254, -453, -762, -1271, -2025, -3225, -4980, -7653, -11472, -17124, -25095, -36507, -52481, -74934, -105876, -148643, -206982, -286437, -393488, -537828, -730362, -987110, -1326579, -1775037, -2363135, -3133227, -4135902, -5438789, -7123452, -9296976
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 29 2018
EXAMPLE
T14a = 1/q - 9*q - 15*q^3 - 33*q^5 - 69*q^7 - 138*q^9 - 254*q^11 - ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q]/eta[q^7])^2; a:= CoefficientList[Series[A - 7*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jun 20 2018 *)
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
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
Terms a(12) onward added by G. C. Greubel, Jun 20 2018
STATUS
approved