A112153 McKay-Thompson series of class 16f for the Monster group.

1, -2, -2, -4, 3, -2, -6, -4, 7, -12, -10, -16, 16, -14, -20, -20, 29, -40, -40, -52, 52, -52, -70, -68, 91, -114, -116, -148, 149, -152, -190, -196, 242, -296, -306, -368, 383, -396, -478, -496, 590, -698, -730, -856, 897, -940, -1096, -1152, 1342, -1548, -1630, -1876, 1975, -2080, -2390, -2516

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, Comm. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

Expansion of sqrt(T8c - 4*q), where T8c = A112145, in powers of q.

Example

T16f = 1/q - 2*q - 2*q^3 - 4*q^5 + 3*q^7 - 2*q^9 - 6*q^11 - 4*q^13 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q^(1/2)*(eta[q]/ eta[q^2])^12; T4B := A + 64*q/A; T8c := Sqrt[(T4B /. {q -> q^4}) + O[q]^nmax]; a:= SeriesCoefficient[Sqrt[-4 *q + T8c + O[q]^nmax], {q, 0, n}]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 28 2018 *)

Crossrefs

Sequence in context: A246953 A045828 A058526 * A112154 A112155 A355476

Adjacent sequences: A112150 A112151 A112152 * A112154 A112155 A112156

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved