A112183 McKay-Thompson series of class 40e for the Monster group.

1, 1, -1, 1, 0, 1, 0, -1, 0, 0, 2, 2, -1, 1, 0, 2, 1, -1, 1, 0, 4, 3, -3, 2, 0, 4, 2, -3, 1, 0, 7, 5, -5, 4, 0, 7, 4, -5, 3, 0, 12, 9, -8, 6, 0, 13, 7, -9, 5, 0, 19, 14, -13, 9, 0, 21, 12, -14, 8, 0, 31, 22, -21, 15, 0, 34, 19, -23, 13, 0, 47, 33, -31, 22, 0, 52, 31, -35, 21, 0, 71, 49, -48, 33, 0, 79, 47

Offset

0,11

Links

G. C. Greubel, Table of n, a(n) for n = 0..1500

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 (T10b + 4)^(1/4), where T10b = A058103, in powers of q. - G. C. Greubel, Jun 28 2018

Example

T40e = 1/q +q^3 -q^7 +q^11 +q^19 -q^27 +2*q^39 +2*q^43 -q^47 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 120;  A:= eta[q]/eta[q^25]; B:= (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]); c:= ((eta[q]*eta[q^2])/( eta[q^5]*eta[q^10]))^2; f5 := (c /. {q -> q^5}); T10b := (2 + c + 5*(c/A^2)*(1 - 1/B)^2 + 25/f5); a:= CoefficientList[Series[ (q*(T10b + 4)  + O[q]^nmax)^(1/4), {q, 0, 110}], q]; Table[a[[n]], {n, 1, 100}] (* G. C. Greubel, Jun 28 2018 *)

Crossrefs

Sequence in context: A081389 A133685 A281492 * A275451 A269317 A119557

Adjacent sequences: A112180 A112181 A112182 * A112184 A112185 A112186

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved