A112190 McKay-Thompson series of class 48e for the Monster group.

1, -1, -1, -1, 0, -1, 0, -1, 1, 0, -2, -1, 1, -1, -1, -2, 2, -2, -2, -1, 1, -2, -2, -2, 4, -3, -4, -4, 2, -4, -2, -4, 5, -4, -6, -5, 5, -6, -5, -7, 8, -7, -8, -7, 6, -8, -8, -9, 13, -12, -14, -13, 10, -14, -10, -14, 17, -14, -20, -17, 17, -19, -18, -22, 24, -24, -26, -24, 22, -26, -26, -29, 37, -34, -39, -38, 32, -40, -34, -42, 48, -44

Offset

0,11

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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(T24d - 2*q) in powers of q, where T24d = A058587. - G. C. Greubel, Jul 01 2018

Example

T48e = 1/q - q - q^3 - q^5 - q^9 - q^13 + q^15 - 2*q^19 - q^21 + q^23 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q*(eta[q^8]*eta[q^12] /(eta[q^4]*eta[q^24]))^3; T24d := A - q^2/A; a:= CoefficientList[ Series[(T24d - 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 01 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^8)*eta(q^12)/(eta(q^4)*eta(q^24)))^3; T24d = A - q^2/A; Vec(sqrt(T24d - 2*q)) \\ G. C. Greubel, Jul 01 2018

Crossrefs

Sequence in context: A094189 A122771 A217710 * A112188 A112189 A112191

Adjacent sequences: A112187 A112188 A112189 * A112191 A112192 A112193

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved