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

%I #25 Jun 28 2018 05:05:02

%S 1,-2,1,-2,4,-6,9,-8,13,-20,22,-28,34,-46,57,-68,87,-104,127,-152,187,

%T -232,267,-318,388,-462,545,-632,753,-896,1043,-1216,1416,-1664,1928,

%U -2228,2597,-2996,3454,-3976,4585,-5286,6031,-6900,7918,-9060,10325,-11720,13372,-15228,17259,-19564

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

%H G. C. Greubel, <a href="/A058553/b058553.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 q^(1/2)*(eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^2 in powers of q. - _G. C. Greubel_, Jun 21 2018

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

%e T20D = 1/q - 2*q + q^3 - 2*q^5 + 4*q^7 - 6*q^9 + 9*q^11 - 8*q^13 + 13*q^15 - ...

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

%o (PARI) q='q+O('q^60); A = (eta(q)*eta(q^5)/(eta(q^2)*eta(q^10)))^2; Vec(A) \\ _G. C. Greubel_, Jun 21 2018

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

%K sign

%O -1,2

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

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