The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A034319 McKay-Thompson series of class 13A for the Monster group with a(0) = 0. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET -1,3 COMMENTS Expansion of Hauptmodul for Gamma_0(13)+. LINKS G. C. Greubel, Table of n, a(n) for n = -1..1000 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 AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 25 15:48 EDT 2023. Contains 361528 sequences. (Running on oeis4.)