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A112196 McKay-Thompson series of class 56a for the Monster group. 1

%I

%S 1,1,1,1,3,2,2,5,6,7,7,9,12,13,16,20,25,27,31,38,44,51,58,69,80,92,

%T 102,118,141,157,177,203,234,261,292,336,382,428,475,540,610,677,757,

%U 852,957,1060,1179,1318,1470,1634,1806,2011,2236,2469,2724,3020,3350

%N McKay-Thompson series of class 56a for the Monster group.

%H G. C. Greubel, <a href="/A112196/b112196.txt">Table of n, a(n) for n = 0..1000</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(T28B + 2) in powers of q, where T28B = A112169. - _G. C. Greubel_, Jul 01 2018

%F a(n) ~ exp(sqrt(2*n/7)*Pi) / (2^(5/4) * 7^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jul 02 2018

%e T56a = 1/q +q +q^3 +q^5 +3*q^7 +2*q^9 +2*q^11 +5*q^13 +6*q^15 +...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; nmax = 70; A:= (eta[q]*eta[q^7]/ (eta[q^4]*eta[q^28])); T28B := 1 + A + 4/A; a:= CoefficientList[Series[ (q*(T28B + 2) + 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^50); A = eta(q)*eta(q^7)/(q*eta(q^4)*eta(q^28)); T28B = A + 1 + 4/A; Vec(sqrt(q*(T28B + 2))) \\ _G. C. Greubel_, Jul 01 2018

%Y Cf. A112169.

%K nonn

%O 0,5

%A _Michael Somos_, Aug 28 2005

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Last modified July 30 17:21 EDT 2021. Contains 346359 sequences. (Running on oeis4.)