A112154 McKay-Thompson series of class 16g for the Monster group.

1, 2, 2, -4, 3, 2, 6, -4, 7, 12, 10, -16, 16, 14, 20, -20, 29, 40, 40, -52, 52, 52, 70, -68, 91, 114, 116, -148, 149, 152, 190, -196, 242, 296, 306, -368, 383, 396, 478, -496, 590, 698, 730, -856, 897, 940, 1096, -1152, 1342, 1548, 1630, -1876, 1975, 2080, 2390, -2516

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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 + 2*q/A, where A = q^(1/2)*(eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2, in powers of q. - G. C. Greubel, Jun 28 2018

Example

T16g = 1/q + 2*q + 2*q^3 - 4*q^5 + 3*q^7 + 2*q^9 + 6*q^11 - 4*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q];  A:= q^(1/2)*(eta[q^4]*eta[q^8]/( eta[q^2]*eta[q^16]))^2; a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2; Vec(A + 2*q/A) \\ G. C. Greubel, Jun 28 2018

Crossrefs

Sequence in context: A045828 A058526 A112153 * A112155 A355476 A328932

Adjacent sequences: A112151 A112152 A112153 * A112155 A112156 A112157

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved