A112189 McKay-Thompson series of class 48d for the Monster group.

1, 1, 1, -1, 0, 1, 0, -1, 1, 0, 2, -1, 1, 1, 1, -2, 2, 2, 2, -1, 1, 2, 2, -2, 4, 3, 4, -4, 2, 4, 2, -4, 5, 4, 6, -5, 5, 6, 5, -7, 8, 7, 8, -7, 6, 8, 8, -9, 13, 12, 14, -13, 10, 14, 10, -14, 17, 14, 20, -17, 17, 19, 18, -22, 24, 24, 26, -24, 22, 26, 26, -29, 37, 34, 39, -38, 32, 40, 34, -42, 48, 44, 54, -49

Offset

0,11

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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 sqrt(T24g + 2*q) in powers of q, where T24g = A112164. - G. C. Greubel, Jul 01 2018

Example

T48d = 1/q + q + q^3 - q^5 + q^9 - q^13 + q^15 + 2*q^19 - q^21 + q^23 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q*(eta[q^4]*eta[q^8]/ (eta[q^12]*eta[q^24])); T24g := A + 3*q^2/A; a:= CoefficientList[ Series[(T24g + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* G. C. Greubel, Jul 01 2018 *)

Prog

(PARI) q='q+O('q^50); A = eta(q^4)*eta(q^8)/(eta(q^12)*eta(q^24)); T24g = A+ 3*q^2/A; Vec(sqrt(T24g + 2*q)) \\ G. C. Greubel, Jul 01 2018

Crossrefs

Sequence in context: A217710 A112190 A112188 * A112191 A328523 A025887

Adjacent sequences: A112186 A112187 A112188 * A112190 A112191 A112192

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved