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McKay-Thompson series of class 16g for the Monster group.
1

%I #12 Jun 28 2018 02:49:19

%S 1,2,2,-4,3,2,6,-4,7,12,10,-16,16,14,20,-20,29,40,40,-52,52,52,70,-68,

%T 91,114,116,-148,149,152,190,-196,242,296,306,-368,383,396,478,-496,

%U 590,698,730,-856,897,940,1096,-1152,1342,1548,1630,-1876,1975,2080,2390,-2516

%N McKay-Thompson series of class 16g for the Monster group.

%H G. C. Greubel, <a href="/A112154/b112154.txt">Table of n, a(n) for n = 0..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>, Comm. 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 A + 2*q/A, where A = q^(1/2)*(eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2, in powers of q. - _G. C. Greubel_, Jun 28 2018

%e T16g = 1/q + 2*q + 2*q^3 - 4*q^5 + 3*q^7 + 2*q^9 + 6*q^11 - 4*q^13 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]*eta[q^8]/( eta[q^2]*eta[q^16]))^2; a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 28 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q^4)*eta(q^8)/(eta(q^2)* eta(q^16)))^2; Vec(A + 2*q/A) \\ _G. C. Greubel_, Jun 28 2018

%K sign

%O 0,2

%A _Michael Somos_, Aug 28 2005