A112177 McKay-Thompson series of class 36h for the Monster group.

1, -2, 0, -1, -2, 0, 0, -2, 0, -2, -6, 0, 2, -6, 0, -1, -8, 0, 2, -14, 0, -2, -16, 0, 3, -20, 0, -4, -32, 0, 4, -38, 0, -4, -46, 0, 7, -66, 0, -7, -78, 0, 6, -96, 0, -10, -130, 0, 11, -154, 0, -11, -186, 0, 14, -244, 0, -16, -288, 0, 17, -346, 0, -21, -440, 0, 22, -518, 0, -24, -618, 0, 32, -768, 0, -34, -902, 0, 34, -1068

Offset

0,2

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 - 2*q/A, where A = q^(1/2)*(eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))), in powers of q. - G. C. Greubel, Jun 26 2018

Example

T36h = 1/q -2*q -q^5 -2*q^7 -2*q^13 -2*q^17 -6*q^19 +2*q^23 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^9]/( eta[q^6]*eta[q^18])); a:= CoefficientList[Series[A - 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 2018 *)

Prog

(PARI) q='q+O('q^70); A = (eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))); Vec(A - 2*q/A) \\ G. C. Greubel, Jun 26 2018

Crossrefs

Sequence in context: A293595 A261249 A058650 * A383673 A115723 A238160

Adjacent sequences: A112174 A112175 A112176 * A112178 A112179 A112180

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved