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 A112195 McKay-Thompson series of class 54d for the Monster group. 1

%I

%S 1,1,-1,1,0,0,1,1,0,2,1,-1,2,1,-1,2,1,-1,4,3,-2,4,2,-1,5,3,-2,7,4,-3,

%T 8,4,-3,9,5,-3,13,8,-6,14,7,-5,16,10,-6,21,12,-9,24,13,-9,27,15,-10,

%U 35,21,-15,39,20,-14,45,26,-17,55,31,-22,62,34,-23,70,39,-26,86,50,-35,96,51,-35,109,62,-41,130

%N McKay-Thompson series of class 54d for the Monster group.

%H G. C. Greubel, <a href="/A112195/b112195.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(T27d) in powers of q, where T27d = A058604. - _G. C. Greubel_, Jul 01 2018

%e T54d = 1/q + q^5 - q^11 + q^17 + q^35 + q^41 + 2*q^53 + q^59 - q^65 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; nmax := 100; A:= q*(eta[q^3]/ eta[q^9])^4; T9b := (A + 9*q^2/A); T27d := (6*q + T9b + O[q]^nmax)^(1/3); a:= CoefficientList[Series[(T27d + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jul 01 2018 *)

%o (PARI) q='q+O('q^80); A = (eta(q^3)/eta(q^9))^4; T9b = A + 9*q^2/A; T27d = (6*q + T9b)^(1/3); Vec(sqrt(T27d)) \\ _G. C. Greubel_, Jul 01 2018

%K sign

%O 0,10

%A _Michael Somos_, Aug 28 2005

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Last modified September 21 06:35 EDT 2021. Contains 347596 sequences. (Running on oeis4.)