A112158 McKay-Thompson series of class 20A for the Monster group.

1, 0, 6, 8, 17, 32, 54, 80, 116, 192, 290, 408, 585, 832, 1192, 1648, 2237, 3072, 4156, 5576, 7414, 9824, 12964, 16896, 22002, 28544, 36794, 47184, 60185, 76736, 97388, 122864, 154615, 194048, 242904, 302800, 376271, 466720, 577176, 711840

Offset

-1,3

Links

G. C. Greubel, Table of n, a(n) for n = -1..1001

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

a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 30 2017

Expansion of -4 + ((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)*eta(q^5)* eta(q^20)))^4 in powers of q. - G. C. Greubel, Jun 06 2018

Example

T20A = 1/q +6*q +8*q^2 +17*q^3 +32*q^4 +54*q^5 +80*q^6 +...

Mathematica

nmax = 60; Flatten[{1, 0, Rest[Rest[CoefficientList[Series[Product[((1 + x^(2*k-1))/((1 + x^(10*k))*(1 - x^(10*k-5))))^4, {k, 1, nmax}], {x, 0, nmax}], x]]]}] (* Vaclav Kotesovec, Apr 30 2017 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^2]*eta[q^10])^2/(eta[q] *eta[q^4]*eta[q^5]*eta[q^20]))^4; a:= CoefficientList[Series[q*(-4 + A), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 06 2018 *)

Prog

(PARI) q='q+O('q^30); F = ((eta(q^2)*eta(q^10))^2/(eta(q)*eta(q^4)* eta(q^5)*eta(q^20)))^4/q; Vec(-4 + F) \\ G. C. Greubel, Jun 06 2018

Crossrefs

Sequence in context: A032411 A345034 A058098 * A270046 A093479 A239396

Adjacent sequences: A112155 A112156 A112157 * A112159 A112160 A112161

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved