A058650 McKay-Thompson series of class 36c for Monster.

1, 2, 0, -1, 2, 0, 0, 2, 0, -2, 6, 0, 2, 6, 0, -1, 8, 0, 2, 14, 0, -2, 16, 0, 3, 20, 0, -4, 32, 0, 4, 38, 0, -4, 46, 0, 7, 66, 0, -7, 78, 0, 6, 96, 0, -10, 130, 0, 11, 154, 0, -11, 186, 0, 14, 244, 0, -16, 288, 0, 17, 346, 0, -21, 440, 0, 22, 518, 0, -24, 618, 0, 32, 768, 0, -34, 902, 0, 34, 1068

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..2500

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 + 2*q/A, where A = q^(1/2)*(eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))), in powers of q. - G. C. Greubel, Jun 23 2018

Example

T36c = 1/q + 2*q - q^5 + 2*q^7 + 2*q^13 - 2*q^17 + 6*q^19 + 2*q^23 + 6*q^25 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^9]/(eta[q^6]*eta[q^18])); a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 23 2018 *)

Prog

(PARI) q='q+O('q^50); A = (eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))); Vec(A + 2*q/A) \\ G. C. Greubel, Jun 23 2018

Crossrefs

Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

Sequence in context: A072574 A293595 A261249 * A112177 A115723 A238160

Adjacent sequences: A058647 A058648 A058649 * A058651 A058652 A058653

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 23 2018

Status

approved