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A058572
McKay-Thompson series of class 24B for Monster.
2
1, 0, 3, 8, 11, 16, 31, 40, 58, 96, 125, 176, 262, 336, 457, 640, 819, 1088, 1464, 1864, 2420, 3168, 3991, 5088, 6533, 8160, 10267, 12976, 16061, 19968, 24912, 30576, 37648, 46464, 56616, 69136, 84518, 102288, 123961, 150304, 180805, 217664, 262042, 313472
OFFSET
-1,3
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4)*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017
Expansion of -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/(eta(q)*eta(q^3) *eta(q^8)*eta(q^24)))^2 in powers of q. - G. C. Greubel, Jan 28 2018
EXAMPLE
T24B = 1/q + 3*q + 8*q^2 + 11*q^3 + 16*q^4 + 31*q^5 + 40*q^6 + 58*q^7 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[-2 + (eta[q^2]*eta[q^4]*eta[q^6]*eta[q^12]/(eta[q]*eta[q^3]*eta[q^8] *eta[q^24]))^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, Jan 28 2018 *)
PROG
(PARI) q='q+O('q^50); A = -2 + (eta(q^2)*eta(q^4)*eta(q^6)*eta(q^12)/( eta(q)*eta(q^3)*eta(q^8)*eta(q^24)))^2/q; Vec(A) \\ G. C. Greubel, Jun 14 2018
CROSSREFS
Cf. A212771 (same sequence except for n=0).
Sequence in context: A190435 A188032 A245978 * A310283 A262290 A184925
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved