A112167 McKay-Thompson series of class 24j for the Monster group.

1, -2, 0, 0, 0, 0, -2, -4, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -2, -12, 0, 0, 0, 0, 4, -18, 0, 0, 0, 0, -4, -28, 0, 0, 0, 0, 5, -44, 0, 0, 0, 0, -6, -64, 0, 0, 0, 0, 9, -92, 0, 0, 0, 0, -12, -132, 0, 0, 0, 0, 13, -186, 0, 0, 0, 0, -16, -256, 0, 0, 0, 0, 21, -352, 0, 0, 0, 0, -26, -476, 0, 0, 0, 0, 29, -638, 0, 0, 0, 0, -36

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

Example

T24j = 1/q - 2*q - 2*q^11 - 4*q^13 + q^23 - 6*q^25 - 2*q^35 - 12*q^37 + ...

Mathematica

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

Prog

(PARI) q='q+O('q^80); A = (eta(q^6)/eta(q^12))^2; Vec(A - 2*q/A) \\ G. C. Greubel, Jun 25 2018

Crossrefs

Sequence in context: A357724 A297934 A112166 * A230571 A037213 A218234

Adjacent sequences: A112164 A112165 A112166 * A112168 A112169 A112170

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved