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 A112191 McKay-Thompson series of class 48f for the Monster group. 1

%I

%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 48f for the Monster group.

%H G. C. Greubel, <a href="/A112191/b112191.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(T24d + 2*q) in powers of q, where T24d = A058587. - _G. C. Greubel_, Jul 01 2018

%e T48f = 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^8] * eta[q^12]/(eta[q^4] * eta[q^24]))^3; T24d := A - q^2/A; mcKayThompson48f := CoefficientList[Series[(T24d + 2*q + O[q]^nmax)^(1/2), {q, 0, 60}], q]; Table[mcKayThompson48f[[n]], {n, 50}] (* _G. C. Greubel_, Jul 01 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q^8)*eta(q^12)/(eta(q^4)*eta(q^24)))^3; T24d = A - q^2/A; Vec(sqrt(T24d + 2*q)) \\ _G. C. Greubel_, Jul 01 2018

%K sign

%O 0,11

%A _Michael Somos_, Aug 28 2005

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)