A112174 McKay-Thompson series of class 36d for the Monster group.

1, 1, 0, 2, -2, 0, 3, 1, 0, 4, 0, 0, 5, 0, 0, 8, -2, 0, 11, 4, 0, 16, -4, 0, 21, 4, 0, 26, -2, 0, 34, 1, 0, 44, -4, 0, 58, 9, 0, 74, -12, 0, 93, 9, 0, 116, -4, 0, 143, 5, 0, 178, -12, 0, 221, 20, 0, 272, -24, 0, 332, 20, 0, 402, -14, 0, 487, 13, 0, 588, -24, 0, 710, 42, 0, 854, -50, 0, 1021, 42, 0

Offset

0,4

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

Example

T36d = 1/q +q +2*q^5 -2*q^7 +3*q^11 +q^13 +4*q^17 +5*q^23 +...

Mathematica

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

Prog

(PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^9)/(eta(q^3)*eta(q^18)))^2; Vec(A+ q/A) \\ G. C. Greubel, Jun 26 2018

Crossrefs

Sequence in context: A294519 A123515 A058648 * A089990 A071427 A248813

Adjacent sequences: A112171 A112172 A112173 * A112175 A112176 A112177

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved