A112214 McKay-Thompson series of class 90a for the Monster group.

1, 0, 1, -1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, -1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2, -1, 0, 3, 1, 0, 3, -1, 0, 4, 1, 0, 5, 0, 0, 5, 0, 0, 5, -1, 0, 6, 2, 0, 7, -2, 0, 8, 2, 0, 9, -1, 0, 10, 0, 0, 11, -1, 0, 12, 3, 0, 14, -2, 0, 15, 1, 0, 17, -1, 0, 18, 1, 0, 20, -2, 0, 22, 4, 0, 25, -5, 0, 28, 3

Offset

-1,24

Links

G. C. Greubel, Table of n, a(n) for n = -1..1500

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^2/A, where A = q*(eta(q^3)*eta(q^18)*eta(q^30)* eta(q^45)/(eta(q^6)*eta(q^9)*eta(q^15)*eta(q^90))), in powers of q. - G. C. Greubel, Jul 02 2018

Example

T90a = 1/q +q -q^2 +q^4 +q^7 +q^10 +q^13 +q^16 +q^19 -q^20 +...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q*(eta[q^3]*eta[q^18]*eta[q^30]* eta[q^45]/(eta[q^6]*eta[q^9]*eta[q^15]*eta[q^90])); T90a := A + q^2/A; a:= CoefficientList[Series[T90a, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jul 02 2018 *)

Prog

(PARI) q='q+O('q^80); A = (eta(q^3)*eta(q^18)*eta(q^30)* eta(q^45)/ (eta(q^6)*eta(q^9)*eta(q^15)*eta(q^90))); Vec(A + q^2/A) \\ G. C. Greubel, Jul 02 2018

Crossrefs

Sequence in context: A110399 A193275 A182033 * A246962 A112608 A058677

Adjacent sequences: A112211 A112212 A112213 * A112215 A112216 A112217

Keyword

sign

Author

Michael Somos, Aug 28 2005

Status

approved