A058611 McKay-Thompson series of class 29A for Monster.

1, 0, 3, 4, 7, 10, 17, 22, 32, 44, 62, 80, 112, 144, 193, 248, 323, 410, 530, 664, 845, 1054, 1324, 1634, 2037, 2498, 3082, 3760, 4601, 5580, 6789, 8186, 9891, 11876, 14271, 17052, 20393, 24260, 28876, 34224, 40557, 47888, 56540, 66516, 78240

Offset

-1,3

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, Commun. Algebra 22, No. 13, 5175-5193 (1994).

Index entries for McKay-Thompson series for Monster simple group

Formula

a(n) ~ exp(4*Pi*sqrt(n/29)) / (sqrt(2)*29^(1/4)*n^(3/4)). - Vaclav Kotesovec, Sep 07 2017

G.f.: - 2 + x^(-1) * ( G(x) * G(x^29) + x^6 * H(x) * H(x^29) )^2 where G() is g.f. of A003114 and H() is g.f. of A003106. - G. C. Greubel, Jun 18 2018

Example

T29A = 1/q + 3*q + 4*q^2 + 7*q^3 + 10*q^4 + 17*q^5 + 22*q^6 + 32*q^7 + ...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; e26B := ((eta[q^2]*eta[q^13])/(eta[q] *eta[q^26]))^2; G[q_] := QPochhammer[q^2, q^5]*QPochhammer[q^3, q^5]* QPochhammer[q^5]/QPochhammer[q]; H[q_] := QPochhammer[q, q^5]* QPochhammer[q^4, q^5]*QPochhammer[q^5]/QPochhammer[q]; a:= CoefficientList[Series[q*(-2 + (1/q)*(G[q]*G[q^29] + q^6*H[q]*H[q^29])^2 ), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* G. C. Greubel, Jun 18 2018 *)

Crossrefs

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

Cf. A136570 (same sequence except for n=0).

Sequence in context: A256912 A378414 A134591 * A357459 A098613 A261037

Adjacent sequences: A058608 A058609 A058610 * A058612 A058613 A058614

Keyword

nonn

Author

N. J. A. Sloane, Nov 27 2000

Extensions

More terms from Michel Marcus, Feb 18 2014

Status

approved