A034319 McKay-Thompson series of class 13A for the Monster group with a(0) = 0.

1, 0, 12, 28, 66, 132, 258, 468, 843, 1428, 2406, 3900, 6253, 9780, 15144, 22980, 34599, 51300, 75430, 109584, 158052, 225676, 320082, 450216, 629329, 873444, 1205514, 1653364, 2256087, 3061620, 4135280, 5557980, 7438170, 9910132

Offset

-1,3

Comments

Expansion of Hauptmodul for Gamma_0(13)+.

Links

G. C. Greubel, Table of n, a(n) for n = -1..1000

Index entries for McKay-Thompson series for Monster simple group

J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

D. Ford, J. McKay and S. P. Norton, More on replicable functions, Comm. Algebra 22, No. 13, 5175-5193 (1994).

I. Chen and N. Yui, Singular values of Thompson series. In Groups, difference sets and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 1996.

Formula

a(n) ~ exp(4*Pi*sqrt(n/13)) / (sqrt(2) * 13^(1/4) * n^(3/4)). - Vaclav Kotesovec, Sep 08 2017

Example

T13A = 1/q + 12*q + 28*q^2 + 66*q^3 + 132*q^4 + 258*q^5 + 468*q^6 +...

Mathematica

eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[2 + (eta[q]/eta[q^13])^2 + 13*(eta[q^13]/eta[q])^2, {q, 0, n}]; Table[a[n], {n, -1, 50}] (* G. C. Greubel, May 04 2018 *)

Prog

(PARI) q='q+O('q^30); Vec(2 + (eta(q)/eta(q^13))^2/q + 13*q*(eta(q^13)/eta(q))^2) \\ G. C. Greubel, May 04 2018

Crossrefs

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

See also A034318.

Sequence in context: A126195 A248547 A164533 * A097427 A039366 A043189

Adjacent sequences: A034316 A034317 A034318 * A034320 A034321 A034322

Keyword

nonn,changed

Author

N. J. A. Sloane

Status

approved