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A058568
McKay-Thompson series of class 22B for Monster.
2
1, 0, 1, -2, 4, -4, 5, -6, 9, -12, 13, -18, 25, -28, 33, -44, 54, -64, 74, -92, 114, -132, 155, -186, 224, -260, 303, -360, 424, -488, 565, -662, 770, -888, 1018, -1180, 1366, -1560, 1780, -2048, 2345, -2668, 3034, -3460, 3946, -4468, 5052, -5734, 6502, -7328, 8255, -9320, 10512, -11808
OFFSET
-1,4
LINKS
D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).
FORMULA
a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/11)) / (2*11^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 08 2017
Expansion of 2 + (eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2 in powers of q. - G. C. Greubel, Jun 18 2018
EXAMPLE
T22B = 1/q + q - 2*q^2 + 4*q^3 - 4*q^4 + 5*q^5 - 6*q^6 + 9*q^7 - 12*q^8 + ...
MATHEMATICA
eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[2 + (eta[q]*eta[q^11]/(eta[q^2]*eta[q^22]))^2, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)
PROG
(PARI) q='q+O('q^50); A = 2 +(eta(q)*eta(q^11)/(eta(q^2)*eta(q^22)))^2/q; Vec(A) \\ G. C. Greubel, Jun 18 2018
CROSSREFS
Cf. A132320 (same sequence except for n=0).
Sequence in context: A133143 A085898 A058679 * A339769 A147534 A118001
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Nov 27 2000
EXTENSIONS
More terms from Michel Marcus, Feb 18 2014
STATUS
approved