A112201 McKay-Thompson series of class 60c for the Monster group.

1, -1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 2, -1, 0, 2, 0, 0, 3, 0, 0, 4, 1, 0, 4, -1, 0, 6, 1, 0, 7, -2, 0, 8, 2, 0, 10, -2, 0, 12, 2, 0, 14, -2, 0, 16, 1, 0, 19, -2, 0, 22, 3, 0, 26, -2, 0, 30, 3, 0, 35, -5, 0, 41, 5, 0, 47, -4, 0, 54, 5, 0, 62, -6, 0, 70, 4, 0, 80, -4, 0, 92, 7, 0, 104, -7, 0, 118, 7, 0, 135

Offset

0,10

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 - q/A, where A = q^(1/2)*(eta(q^6)*eta(q^15)/( eta(q^3)* eta(q^30))), in powers of q. - G. C. Greubel, Jun 28 2018

Example

T60c = 1/q -q +q^5 +q^7 +q^11 +2*q^17 +q^19 +2*q^23 -q^25 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^15]/( eta[q^3]*eta[q^30])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}]  (* G. C. Greubel, Jun 28 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^6)*eta(q^15)/( eta(q^3)* eta(q^30))); Vec(A - q/A) \\ G. C. Greubel, Jun 28 2018

Crossrefs

Sequence in context: A095734 A137269 A343348 * A112203 A196279 A132798

Adjacent sequences: A112198 A112199 A112200 * A112202 A112203 A112204

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved