A112166 McKay-Thompson series of class 24i 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

T24i = 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: A174469 A357724 A297934 * A112167 A230571 A037213

Adjacent sequences: A112163 A112164 A112165 * A112167 A112168 A112169

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved