A112191 - OEIS

A112191

McKay-Thompson series of class 48f 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, -54, 49

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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

T48f = 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; mcKayThompson48f := CoefficientList[Series[(T24d + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[mcKayThompson48f[[n]], {n, 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: A112190 A112188 A112189 * A328523 A025887 A025882

Adjacent sequences: A112188 A112189 A112190 * A112192 A112193 A112194

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved