A112155 McKay-Thompson series of class 16h 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

T16h = 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, n}]; Table[a[[n]], {n, 0, 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: A058526 A112153 A112154 * A355476 A328932 A341148

Adjacent sequences: A112152 A112153 A112154 * A112156 A112157 A112158

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved