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%I #11 Jul 01 2018 19:35:15
%S 1,1,1,-1,0,1,0,-1,1,0,2,-1,1,1,1,-2,2,2,2,-1,1,2,2,-2,4,3,4,-4,2,4,2,
%T -4,5,4,6,-5,5,6,5,-7,8,7,8,-7,6,8,8,-9,13,12,14,-13,10,14,10,-14,17,
%U 14,20,-17,17,19,18,-22,24,24,26,-24,22,26,26,-29,37,34,39,-38,32,40,34,-42,48,44,54,-49
%N McKay-Thompson series of class 48d for the Monster group.
%H G. C. Greubel, <a href="/A112189/b112189.txt">Table of n, a(n) for n = 0..5000</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 sqrt(T24g + 2*q) in powers of q, where T24g = A112164. - _G. C. Greubel_, Jul 01 2018
%e T48d = 1/q + q + q^3 - q^5 + q^9 - q^13 + q^15 + 2*q^19 - q^21 + q^23 + ...
%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax = 100; A:= q*(eta[q^4]*eta[q^8]/ (eta[q^12]*eta[q^24])); T24g := A + 3*q^2/A; a:= CoefficientList[ Series[(T24g + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jul 01 2018 *)
%o (PARI) q='q+O('q^50); A = eta(q^4)*eta(q^8)/(eta(q^12)*eta(q^24)); T24g = A+ 3*q^2/A; Vec(sqrt(T24g + 2*q)) \\ _G. C. Greubel_, Jul 01 2018
%K sign
%O 0,11
%A _Michael Somos_, Aug 28 2005
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