A112159 McKay-Thompson series of class 20C for the Monster group.

1, 0, 1, -2, 2, 2, -1, 0, -4, 2, 5, -2, 0, -8, 2, 8, -3, 2, -14, 6, 14, -6, 4, -24, 12, 24, -11, 4, -40, 16, 38, -16, 5, -62, 24, 60, -24, 10, -94, 40, 91, -38, 18, -144, 62, 136, -57, 24, -214, 88, 201, -82, 30, -308, 122, 288, -117, 48, -440, 180, 410, -168, 74, -624, 262, 578, -238, 96, -874, 356

Offset

-1,4

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

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

Index entries for McKay-Thompson series for Monster simple group

Formula

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

Example

T20C = 1/q + q - 2*q^2 + 2*q^3 + 2*q^4 - q^5 - 4*q^7 + 2*q^8 + 5*q^9 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q];  a:= CoefficientList[Series[q*(2 + (eta[q]*eta[q^4]*eta[q^10]/(eta[q^2]*eta[q^5]*eta[q^20]))^2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 06 2018 *)

Prog

(PARI) q='q+O('q^80); F = 2 + (eta(q)*eta(q^4)*eta(q^10)/(eta(q^2) *eta(q^5)*eta(q^20)))^2/q; Vec(F) \\ G. C. Greubel, Jun 06 2018

Crossrefs

Sequence in context: A108839 A114898 A223903 * A058101 A132980 A106823

Adjacent sequences: A112156 A112157 A112158 * A112160 A112161 A112162

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved