A112171 McKay-Thompson series of class 32c for the Monster group.

1, 2, 0, 0, -1, 2, 0, 0, -1, 4, 0, 0, 0, 6, 0, 0, 1, 8, 0, 0, 0, 12, 0, 0, -1, 18, 0, 0, 1, 24, 0, 0, 2, 32, 0, 0, -1, 44, 0, 0, -2, 58, 0, 0, 1, 76, 0, 0, 2, 100, 0, 0, -1, 128, 0, 0, -3, 164, 0, 0, 1, 210, 0, 0, 4, 264, 0, 0, -2, 332, 0, 0, -5, 416, 0, 0, 2, 516, 0, 0, 5, 640, 0, 0, -2, 790, 0, 0

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^4)/eta(q^16)), in powers of q. - G. C. Greubel, Jun 26 2018

Example

T32c = 1/q +2*q -q^7 +2*q^9 -q^15 +4*q^17 +6*q^25 +q^31 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]/eta[q^16]); a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) q='q+O('q^80); A = eta(q^4)/eta(q^16); Vec(A + 2*q/A) \\ G. C. Greubel, Jun 26 2018

Crossrefs

Sequence in context: A357648 A025873 A208589 * A112172 A093085 A339059

Adjacent sequences: A112168 A112169 A112170 * A112172 A112173 A112174

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved