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A112171 McKay-Thompson series of class 32c for the Monster group. 1

%I

%S 1,2,0,0,-1,2,0,0,-1,4,0,0,0,6,0,0,1,8,0,0,0,12,0,0,-1,18,0,0,1,24,0,

%T 0,2,32,0,0,-1,44,0,0,-2,58,0,0,1,76,0,0,2,100,0,0,-1,128,0,0,-3,164,

%U 0,0,1,210,0,0,4,264,0,0,-2,332,0,0,-5,416,0,0,2,516,0,0,5,640,0,0,-2,790,0,0

%N McKay-Thompson series of class 32c for the Monster group.

%H G. C. Greubel, <a href="/A112171/b112171.txt">Table of n, a(n) for n = 0..2500</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^16)), in powers of q. - _G. C. Greubel_, Jun 26 2018

%e T32c = 1/q +2*q -q^7 +2*q^9 -q^15 +4*q^17 +6*q^25 +q^31 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^4]/eta[q^16]); a:= CoefficientList[Series[A + 2*q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 26 2018 *)

%o (PARI) q='q+O('q^80); A = eta(q^4)/eta(q^16); Vec(A + 2*q/A) \\ _G. C. Greubel_, Jun 26 2018

%K sign

%O 0,2

%A _Michael Somos_, Aug 28 2005

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Last modified March 25 03:50 EDT 2019. Contains 321450 sequences. (Running on oeis4.)