A112186 McKay-Thompson series of class 48a 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

T48a = 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, 30}]  (* G. C. Greubel, Jun 19 2018 *)

Prog

(PARI) q='q+O('q^50); 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: A092953 A058574 A112165 * A112187 A341621 A074093

Adjacent sequences: A112183 A112184 A112185 * A112187 A112188 A112189

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved