A112147 McKay-Thompson series of class 12A for the Monster group.

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

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 A331551

Adjacent sequences: A112144 A112145 A112146 * A112148 A112149 A112150

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved