|
%I #19 May 04 2018 18:25:39
%S 1,0,12,28,66,132,258,468,843,1428,2406,3900,6253,9780,15144,22980,
%T 34599,51300,75430,109584,158052,225676,320082,450216,629329,873444,
%U 1205514,1653364,2256087,3061620,4135280,5557980,7438170,9910132
%N McKay-Thompson series of class 13A for the Monster group with a(0) = 0.
%C Expansion of Hauptmodul for Gamma_0(13)+.
%H G. C. Greubel, <a href="/A034319/b034319.txt">Table of n, a(n) for n = -1..1000</a>
%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. Algebra 22, No. 13, 5175-5193 (1994).
%H I. Chen and N. Yui, <a href="http://www.math.sfu.ca/~ichen/pub.html">Singular values of Thompson series</a>. 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.
%F a(n) ~ exp(4*Pi*sqrt(n/13)) / (sqrt(2) * 13^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017
%e T13A = 1/q + 12*q + 28*q^2 + 66*q^3 + 132*q^4 + 258*q^5 + 468*q^6 +...
%t 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 *)
%o (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
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y See also A034318.
%K nonn
%O -1,3
%A _N. J. A. Sloane_
|
