A112178 McKay-Thompson series of class 36i for the Monster group.

1, -1, 0, -1, -1, 0, 0, -1, 0, 1, 0, 0, -1, 0, 0, -1, -1, 0, 2, -1, 0, -2, -2, 0, 0, -1, 0, 2, -1, 0, -2, -1, 0, -1, -2, 0, 4, -3, 0, -4, -3, 0, 0, -3, 0, 5, -2, 0, -4, -2, 0, -2, -3, 0, 8, -5, 0, -7, -6, 0, -1, -5, 0, 9, -4, 0, -8, -4, 0, -3, -6, 0, 14, -9, 0, -13, -10, 0, -2, -9, 0, 16, -8, 0, -14, -8, 0, -5, -11, 0, 24, -14, 0, -21, -16, 0, -3

Offset

0,19

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 A - q/A, where A = q^(1/2)*(eta(q^3)*eta(q^18)^2* eta(q^27)/(eta(q^6)*eta(q^9)^2*eta(q^54))), in powers of q. - G. C. Greubel, Jun 16 2018

Example

T36i = 1/q -q -q^5 -q^7 -q^13 +q^17 -q^23 -q^29 -q^31 +2*q^35 +...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^18]^2* eta[q^27]/(eta[q^6]*eta[q^9]^2*eta[q^54])); a:=CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 16 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^18)^2* eta(q^27)/(eta(q^6) *eta(q^9)^2*eta(q^54))); Vec(A - q/A) \\ G. C. Greubel, Jun 16 2018

Crossrefs

Sequence in context: A356262 A281228 A284575 * A134663 A000925 A258279

Adjacent sequences: A112175 A112176 A112177 * A112179 A112180 A112181

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved