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McKay-Thompson series of class 20b for Monster.
1

%I #22 Jun 28 2018 04:31:09

%S 1,4,3,16,20,48,55,108,141,248,326,516,662,1048,1335,2000,2547,3672,

%T 4689,6588,8379,11500,14513,19644,24688,32896,41115,53964,67301,87312,

%U 108385,139124,171876,218852,269284,339996,416665,522104,637698,793704,965989,1194888,1448933,1782800

%N McKay-Thompson series of class 20b for Monster.

%H G. C. Greubel, <a href="/A058557/b058557.txt">Table of n, a(n) for n = -1..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 + q/A, where A = q^(1/2)*(eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3, in powers of q. - _G. C. Greubel_, Jun 21 2018

%F a(n) ~ exp(2*Pi*sqrt(n/5)) / (2 * 5^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T20b = 1/q + 4*q + 3*q^3 + 16*q^5 + 20*q^7 + 48*q^9 + 55*q^11 + 108*q^13 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A := q^(1/2)*(eta[q^2]*eta[q^5]/(eta[q]*eta[q^10]))^3; a:= CoefficientList[Series[A + q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 21 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q^2)*eta(q^5)/(eta(q)* eta(q^10)))^3; Vec(A + q/A) \\ _G. C. Greubel_, Jun 21 2018

%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.

%K nonn

%O -1,2

%A _N. J. A. Sloane_, Nov 27 2000

%E Terms a(12) onward added by _G. C. Greubel_, Jun 21 2018