A058560 McKay-Thompson series of class 20e for Monster.

1, 2, -1, 0, 3, 0, 3, -4, 0, 2, 3, 8, -4, 0, 9, 4, 12, -10, 0, 8, 10, 26, -14, 0, 23, 10, 35, -28, 0, 26, 26, 64, -39, 0, 57, 28, 89, -66, 0, 64, 56, 150, -91, 0, 125, 66, 202, -148, 0, 148, 120, 320, -198, 0, 259, 144, 429, -302, 0, 312, 243, 648, -405, 0, 511, 292, 860, -600, 0, 622

Offset

-1,2

Links

G. C. Greubel, Table of n, a(n) for n = -1..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 (T10b + 4)^(1/2), where T10b = A058103, in powers of q. - G. C. Greubel, Jun 21 2018

Example

T20e = 1/q + 2*q - q^3 + 3*q^7 + 3*q^11 - 4*q^13 + 2*q^17 + 3*q^19 + ...

Mathematica

eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100;  A:= eta[q]/eta[q^25]; B:= (eta[q^2]*eta[q^25])/(eta[q]*eta[q^50]); c := ((eta[q]*eta[q^2])/( eta[q^5]*eta[q^10]))^2; d:= ((eta[q^5]*eta[q^10])/( eta[q^25]*eta[q^50]) )^2; T10b := (2 + c + 5*(c/(A)^2)*(1 - 1/B)^2 + 25/d); a:= CoefficientList[Series[(q*(T10b + 4) + O[q]^nmax)^(1/2), {q, 0, nmax}], q]; Table[a[[n]], {n, 1, nmax}] (* G. C. Greubel, Jun 21 2018, fixed by Vaclav Kotesovec, Jul 03 2018 *)

Crossrefs

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

Sequence in context: A210869 A123973 A098493 * A131047 A366548 A143714

Adjacent sequences: A058557 A058558 A058559 * A058561 A058562 A058563

Keyword

sign

Author

N. J. A. Sloane, Nov 27 2000

Extensions

Terms a(12) onward added by G. C. Greubel, Jun 21 2018

Status

approved