A112151 McKay-Thompson series of class 16b for the Monster group.

1, 4, -2, 8, -1, 20, 2, 40, 3, 72, -2, 128, -4, 220, 4, 360, 5, 576, -8, 904, -8, 1384, 10, 2088, 11, 3108, -12, 4552, -15, 6592, 18, 9448, 22, 13392, -26, 18816, -29, 26216, 34, 36224, 38, 49700, -42, 67728, -51, 91688, 56, 123392, 66, 165128, -78, 219784, -85, 291072

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of A + 4*q/A, where A = q^(1/2)*(eta(q^2)/eta(q^8))^2, in powers of q. - G. C. Greubel, Jun 16 2018

Example

T16b = 1/q +4*q -2*q^3 +8*q^5 -q^7 +20*q^9 +2*q^11 +40*q^13 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; e16d := q^(1/4)*(eta[q]/eta[q^4])^2;
a[n_]:= SeriesCoefficient[(e16d /. {q -> q^2}) + 4*q/(e16d /. {q -> q^2}), {q, 0, n}]; Table[a[n], {n, 0, 50}] (* G. C. Greubel, Feb 13 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^2)/eta(q^8))^2; Vec(A + 4*q/A) \\ G. C. Greubel, Jun 16 2018

Crossrefs

Sequence in context: A241005 A029841 A112143 * A112152 A211883 A083489

Adjacent sequences: A112148 A112149 A112150 * A112152 A112153 A112154

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved