A112187 McKay-Thompson series of class 48b for the Monster group.

1, -1, 1, 1, 2, 1, 2, -1, 3, 0, 4, 1, 5, -1, 7, 0, 8, 0, 10, -1, 13, 2, 16, 0, 20, -3, 24, 2, 30, 2, 36, -4, 43, 0, 52, 3, 61, -2, 73, 1, 86, 1, 102, -3, 120, 4, 140, 1, 165, -8, 192, 5, 224, 6, 260, -10, 301, 2, 348, 7, 401, -7, 462, 2, 530, 2, 608, -8, 696, 10, 796, 3, 909, -18, 1035, 12

Offset

0,5

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 - q/A, where A = q^(1/2)*(eta(q^6)*eta(q^8))/(eta(q^2)* eta(q^24)), in powers of q. - G. C. Greubel, Jun 19 2018

Example

T48b = 1/q - q + q^3 + q^5 + 2*q^7 + q^9 + 2*q^11 - q^13 + 3*q^15 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^6]*eta[q^8])/( eta[q^2]*eta[q^24]); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 80}] (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^8))/(eta(q^2)*eta(q^24)); Vec(A - q/A) \\ G. C. Greubel, Jun 19 2018

Crossrefs

Sequence in context: A058574 A112165 A112186 * A341621 A074093 A324286

Adjacent sequences: A112184 A112185 A112186 * A112188 A112189 A112190

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved