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A112147 McKay-Thompson series of class 12A for the Monster group. 2
1, 0, 15, 32, 87, 192, 343, 672, 1290, 2176, 3705, 6336, 10214, 16320, 25905, 39936, 61227, 92928, 138160, 204576, 300756, 435328, 626727, 897408, 1271205, 1790592, 2508783, 3487424, 4824825, 6641664, 9083400, 12371904, 16778784 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = -1..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

FORMULA

Expansion of -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3)*eta(q^4) *eta(q^12))^6) in powers of q. - G. C. Greubel, Jun 19 2018

a(n) ~ exp(2*Pi*sqrt(n/3)) / (2 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 28 2018

EXAMPLE

T12A = 1/q + 15*q + 32*q^2 + 87*q^3 + 192*q^4 + 343*q^5 + 672*q^6 + ...

MATHEMATICA

eta[q_]:= q^(1/24)*QPochhammer[q]; a := CoefficientList[Series[-6 + (eta[q^2]*eta[q^6])^12/((eta[q]*eta[q^3]*eta[q^4]*eta[q^12])^6), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 19 2018 *)

PROG

(PARI) q='q+O('q^50); A = -6 + (eta(q^2)*eta(q^6))^12/((eta(q)*eta(q^3) *eta(q^4)*eta(q^12))^6)/q; Vec(A) \\ G. C. Greubel, Jun 19 2018

CROSSREFS

Sequence in context: A061047 A098848 A055809 * A007256 A199743 A180815

Adjacent sequences:  A112144 A112145 A112146 * A112148 A112149 A112150

KEYWORD

nonn

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved

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Last modified August 14 04:36 EDT 2018. Contains 313748 sequences. (Running on oeis4.)