A112152 - OEIS

A112152

McKay-Thompson series of class 16c 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

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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 A - 4*q/A, where A = q^(1/2)*(eta(q^2)/eta(q^8))^2, in powers of q. - G. C. Greubel, Jun 26 2018

EXAMPLE

T16c = 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]; A:= q^(1/2)*(eta[q^2]/eta[q^8])^2; a:= CoefficientList[Series[A - 4*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 26 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 26 2018

CROSSREFS

Cf. A029841, A112143, A112151.

Sequence in context: A029841 A112143 A112151 * A211883 A083489 A065464

Adjacent sequences: A112149 A112150 A112151 * A112153 A112154 A112155

KEYWORD

sign

AUTHOR

Michael Somos, Aug 28 2005

STATUS

approved