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McKay-Thompson series of class 36h for the Monster group.
1

%I #11 Jun 26 2018 04:55:25

%S 1,-2,0,-1,-2,0,0,-2,0,-2,-6,0,2,-6,0,-1,-8,0,2,-14,0,-2,-16,0,3,-20,

%T 0,-4,-32,0,4,-38,0,-4,-46,0,7,-66,0,-7,-78,0,6,-96,0,-10,-130,0,11,

%U -154,0,-11,-186,0,14,-244,0,-16,-288,0,17,-346,0,-21,-440,0,22,-518,0,-24,-618,0,32,-768,0,-34,-902,0,34,-1068

%N McKay-Thompson series of class 36h for the Monster group.

%H G. C. Greubel, <a href="/A112177/b112177.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^3)*eta(q^9)/(eta(q^6)* eta(q^18))), in powers of q. - _G. C. Greubel_, Jun 26 2018

%e T36h = 1/q -2*q -q^5 -2*q^7 -2*q^13 -2*q^17 -6*q^19 +2*q^23 +...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^3]*eta[q^9]/( eta[q^6]*eta[q^18])); 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^70); A = (eta(q^3)*eta(q^9)/(eta(q^6)* eta(q^18))); Vec(A - 2*q/A) \\ _G. C. Greubel_, Jun 26 2018

%K sign

%O 0,2

%A _Michael Somos_, Aug 28 2005