A112162 McKay-Thompson series of class 24b for the Monster group.

1, 1, 7, 9, 10, 23, 38, 47, 75, 112, 148, 217, 293, 385, 553, 728, 928, 1272, 1670, 2111, 2765, 3566, 4504, 5784, 7300, 9123, 11592, 14458, 17838, 22342, 27668, 33884, 41843, 51344, 62548, 76515, 92989, 112514, 136687, 164961, 198190

Offset

0,3

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^3)*eta(q^4)/(eta(q)* eta(q^12)))^2, in powers of q. - G. C. Greubel, Jun 25 2018

a(n) ~ exp(sqrt(2*n/3)*Pi) / (2^(5/4) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Jun 27 2018

Example

T24b = 1/q + q + 7*q^3 + 9*q^5 + 10*q^7 + 23*q^9 + 38*q^11 + 47*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^3]*eta[q^4]/(eta[q]*eta[q^12]))^2; a := CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 25 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^4)/(eta(q)*eta(q^12)))^2; Vec(A - q/A) \\ G. C. Greubel, Jun 25 2018

Crossrefs

Sequence in context: A095034 A118621 A117933 * A058483 A176326 A283056

Adjacent sequences: A112159 A112160 A112161 * A112163 A112164 A112165

Keyword

nonn

Author

Michael Somos, Aug 28 2005

Status

approved