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A058535 McKay-Thompson series of class 18E for Monster. 2

%I #17 Jun 26 2018 08:41:33

%S 1,0,6,13,24,42,73,120,192,299,456,684,1007,1464,2100,2976,4176,5802,

%T 7993,10920,14808,19946,26688,35496,46944,61752,80826,105286,136536,

%U 176304,226725,290448,370704,471467,597600,755028,950980,1194216

%N McKay-Thompson series of class 18E for Monster.

%H G. C. Greubel, <a href="/A058535/b058535.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>, Commun. 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 + 2 + 6/A, where A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2) *eta(q^3)*eta(q^18)^2)), in powers of q. - _G. C. Greubel_, Jun 18 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n)/3) / (2^(3/4) * sqrt(3) * n^(3/4)). - _Vaclav Kotesovec_, Jun 26 2018

%e T18E = 1/q + 6*q + 13*q^2 + 24*q^3 + 42*q^4 + 73*q^5 + 120*q^6 + 192*q^7 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; e18D3:= (eta[q]^2*eta[q^6]*eta[q^9]/( eta[q^2]*eta[q^3]*eta[q^18]^2)); a := CoefficientList[Series[2 + e18D3 + 6/e18D3, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 18 2018 *)

%o (PARI) q='q+O('q^50); A = (eta(q)^2*eta(q^6)*eta(q^9)/(eta(q^2)*eta(q^3) *eta(q^18)^2))/q; Vec(A + 2 + 6/A) \\ _G. C. Greubel_, Jun 18 2018

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

%Y Cf. A128517 (same sequence except for n=0).

%K nonn

%O -1,3

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

%E More terms from _Michel Marcus_, Feb 19 2014

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)