A112164 McKay-Thompson series of class 24g for the Monster group.

1, 3, -1, 3, -2, 9, 2, 9, -1, 24, 0, 27, 5, 51, -3, 60, -4, 108, 6, 129, -3, 210, -4, 252, 12, 393, -8, 474, -10, 702, 16, 852, -9, 1224, -8, 1485, 29, 2070, -17, 2511, -22, 3429, 38, 4155, -20, 5556, -20, 6723, 61, 8856, -36, 10695, -44, 13878, 80, 16722, -43, 21450, -44, 25785

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..2500

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 A + 3*q/A, where A = q^(1/2)*eta(q^2)*eta(q^4)/(eta(q^6) * eta(q^12)), in powers of q. - G. C. Greubel, Jun 25 2018

Example

T24g = 1/q + 3*q - q^3 + 3*q^5 - 2*q^7 + 9*q^9 + 2*q^11 + 9*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^4]/( eta[q^6]*eta[q^12]));  a:= CoefficientList[Series[A + 3*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) q='q+O('q^60); A = eta(q^2)*eta(q^4)/(eta(q^6)*eta(q^12)); Vec(A + 3*q/A) \\ G. C. Greubel, Jun 25 2018

Crossrefs

Sequence in context: A248947 A133916 A058589 * A300580 A075676 A298262

Adjacent sequences: A112161 A112162 A112163 * A112165 A112166 A112167

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved