A112172 McKay-Thompson series of class 32d for the Monster group.

1, -2, 0, 0, -1, -2, 0, 0, -1, -4, 0, 0, 0, -6, 0, 0, 1, -8, 0, 0, 0, -12, 0, 0, -1, -18, 0, 0, 1, -24, 0, 0, 2, -32, 0, 0, -1, -44, 0, 0, -2, -58, 0, 0, 1, -76, 0, 0, 2, -100, 0, 0, -1, -128, 0, 0, -3, -164, 0, 0, 1, -210, 0, 0, 4, -264, 0, 0, -2, -332, 0, 0, -5, -416, 0, 0, 2, -516, 0, 0, 5, -640, 0, 0, -2, -790, 0, 0

Offset: 0

Author

Michael Somos, Aug 28 2005

Keywords

• sign

Examples

			T32d = 1/q - 2*q - q^7 - 2*q^9 - q^15 - 4*q^17 - 6*q^25 + q^31 + ...
		

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).
• Index entries for McKay-Thompson series for Monster simple group

Programs

Mathematica

QP = QPochhammer; G[q_]:= QP[q^2, q^5]*QP[q^3, q^5]*QP[q^5, q^5]/QP[q, q]; H[q_]:= QP[q, q^5]*QP[q^4, q^5]*QP[q^5, q^5]/QP[q, q]; a[n_]:= SeriesCoefficient[(G[q]*G[q^19] + q^4*H[q]*H[q^19])^3/q - 3, {q,0,n}]; Table[A058549[n], {n,-1,50}] (* G. C. Greubel, Feb 18 2018 *)
eta[q_]:= q^(1/24)*QPochhammer[q]; A := q^(1/2)*eta[q^4]/eta[q^16]; a:=
CoefficientList[Series[(A - 2*q/A), {q, 0, 100}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)

PARI

q='q+O('q^50); A = eta(q^4)/eta(q^16); Vec(A - 2*q/A) \\ G. C. Greubel, Jun 16 2018

Formula

Expansion of A - 2*q/A, where A = q^(1/2)*eta(q^4)/eta(q^16), in powers of q. - G. C. Greubel, Jun 16 2018