A112198 McKay-Thompson series of class 56c for the Monster group.

1, -1, 1, 1, 1, 0, 2, 1, 2, -1, 3, 1, 4, -1, 4, 0, 5, -1, 7, 2, 8, -1, 10, 1, 12, -2, 14, 2, 17, -3, 21, 3, 24, -3, 28, 4, 34, -4, 39, 4, 46, -5, 53, 4, 61, -4, 71, 6, 82, -6, 94, 7, 108, -7, 124, 8, 142, -11, 162, 11, 185, -10, 210, 12, 238, -14, 271, 15, 306, -15, 345, 14, 390, -17, 439, 20, 494

Offset

0,7

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^4)*eta(q^14)/(eta(q^2)* eta(q^28))), in powers of q. - G. C. Greubel, Jul 01 2018

Example

T56c = 1/q - q + q^3 + q^5 + q^7 + 2*q^11 + q^13 + 2*q^15 - q^17 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^14]/(eta[q^2]*eta[q^28])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^14)/(eta(q^2)*eta(q^28)); Vec(A - q/A) \\ G. C. Greubel, Jul 01 2018

Crossrefs

Sequence in context: A263111 A260438 A112197 * A326850 A303756 A105259

Adjacent sequences: A112195 A112196 A112197 * A112199 A112200 A112201

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved