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A058705 McKay-Thompson series of class 52A for Monster. 2

%I

%S 1,0,2,2,3,2,5,4,7,6,12,10,17,14,23,24,34,32,47,46,64,64,87,88,117,

%T 118,156,160,207,212,271,280,352,366,455,476,587,612,748,788,950,1004,

%U 1205,1274,1515,1608,1900,2020,2373,2524,2951,3148,3659,3902,4521,4830,5563,5948,6827,7306,8353

%N McKay-Thompson series of class 52A for Monster.

%H G. C. Greubel, <a href="/A058705/b058705.txt">Table of n, a(n) for n = -1..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 A - q/A, where A = q^(1/2)*(eta(q^2)*eta(q^13)/(eta(q)* eta(q^26))), in powers of q. - _G. C. Greubel_, Jun 27 2018

%F a(n) ~ exp(2*Pi*sqrt(n/13)) / (2 * 13^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T52A = 1/q + 2*q^3 + 2*q^5 + 3*q^7 + 2*q^9 + 5*q^11 + 4*q^13 + 7*q^15 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= q^(1/2)*(eta[q^2]*eta[q^13]/(eta[q]*eta[q^26])); a:= CoefficientList[Series[A - q/A, {q, 0, 60}], q]; Table[a[[n]], {n, 0, 50}] (* _G. C. Greubel_, Jun 27 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q^2)*eta(q^13)/(eta(q)*eta(q^26)); Vec(A - q/A) \\ _G. C. Greubel_, Jun 27 2018

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

%K nonn

%O -1,3

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

%E Terms a(12) onward added by _G. C. Greubel_, Jun 27 2018

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Last modified February 16 19:29 EST 2019. Contains 320167 sequences. (Running on oeis4.)