A112181 McKay-Thompson series of class 40c for the Monster group.

1, 2, -1, 2, 0, 2, -1, 4, 1, 4, -2, 8, 2, 10, -1, 12, 3, 16, -3, 20, 3, 28, -3, 34, 4, 42, -5, 52, 5, 64, -7, 84, 8, 100, -8, 120, 9, 148, -10, 176, 13, 218, -15, 260, 14, 308, -17, 368, 20, 436, -23, 524, 24, 616, -26, 724, 31, 852, -34, 996, 38, 1178, -41, 1370, 46, 1592, -52, 1856, 55

Offset

0,2

Comments

Essentially the same as A058666. - R. J. Mathar, Mar 23 2012

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^2)*eta(q^10)/( eta(q^4)* eta(q^20))), in powers of q. - G. C. Greubel, Jun 26 2018

Example

T40c = 1/q +2*q -q^3 +2*q^5 +2*q^9 -q^11 +4*q^13 +q^15 +4*q^17 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^10]/( eta[q^4]*eta[q^20])); 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^50); A = (eta(q^2)*eta(q^10)/(eta(q^4)*eta(q^20))); Vec(A + 2*q/A) \\ G. C. Greubel, Jun 26 2018

Crossrefs

Sequence in context: A322019 A077883 A058666 * A151676 A151684 A118207

Adjacent sequences: A112178 A112179 A112180 * A112182 A112183 A112184

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved