A112197 McKay-Thompson series of class 56b 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

T56b = 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: A361734 A263111 A260438 * A112198 A326850 A303756

Adjacent sequences: A112194 A112195 A112196 * A112198 A112199 A112200

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved