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McKay-Thompson series of class 30D for Monster.
2

%I #19 Jun 26 2018 08:42:10

%S 1,0,3,4,5,10,15,22,29,36,53,72,99,128,160,212,272,354,448,556,703,

%T 874,1096,1356,1662,2050,2501,3060,3716,4492,5444,6550,7882,9436,

%U 11262,13460,16013,19034,22536,26616,31450,37048,43602,51164,59905

%N McKay-Thompson series of class 30D for Monster.

%H G. C. Greubel, <a href="/A058615/b058615.txt">Table of n, a(n) for n = -1..1000</a>

%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Commun. Algebra 22, No. 13, 5175-5193 (1994).

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of -2 + ((eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15))/(eta(q)* eta(q^5)*eta(q^6)*eta(q^30)))^2 in powers of q. - _G. C. Greubel_, Jun 18 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/15)) / (2^(3/4) * 15^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018

%e T30D = 1/q + 3*q + 4*q^2 + 5*q^3 + 10*q^4 + 15*q^5 + 22*q^6 + 29*q^7 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A:= ((eta[q^2]*eta[q^3]*eta[q^10]* eta[q^15])/(eta[q]*eta[q^5]*eta[q^6]*eta[q^30]))^2; a:= CoefficientList[Series[-2 + A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)

%o (PARI) q='q+O('q^50); A = -2 + ((eta(q^2)*eta(q^3)*eta(q^10)*eta(q^15))/( eta(q)* eta(q^5)*eta(q^6)*eta(q^30)))^2/q; Vec(A) \\ _G. C. Greubel_, Jun 18 2018

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

%Y Cf. A205962 (same sequence except for n=0).

%K nonn

%O -1,3

%A _N. J. A. Sloane_, Nov 27 2000

%E More terms from _Michel Marcus_, Feb 18 2014