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A058597 McKay-Thompson series of class 26B for Monster. 2

%I #24 Jun 14 2018 20:24:48

%S 1,0,3,6,9,14,22,32,46,66,93,128,176,236,315,420,550,718,932,1198,

%T 1534,1956,2476,3120,3919,4896,6095,7562,9341,11504,14126,17284,21090,

%U 25666,31140,37692,45515,54818,65878,79000,94523,112872,134522,160004

%N McKay-Thompson series of class 26B for Monster.

%H G. C. Greubel, <a href="/A058597/b058597.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 a(n) ~ exp(2*Pi*sqrt(2*n/13)) / (2^(3/4) * 13^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Sep 08 2017

%F Expansion of -2 + ((eta(q^2)*eta(q^13))/(eta(q)* eta(q^26)))^2 in powers of q. - _G. C. Greubel_, Feb 18 2018

%e T26B = 1/q + 3*q + 6*q^2 + 9*q^3 + 14*q^4 + 22*q^5 + 32*q^6 + 46*q^7 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; e26B:= ((eta[q^2]*eta[q^13])/(eta[q]* eta[q^26]))^2; Table[SeriesCoefficient[-2 + e26B, {q, 0, n}], {n, -1, 50}] (* _G. C. Greubel_, Feb 18 2018 *)

%o (PARI) q='q+O('q^50); A = -2 + ((eta(q^2)*eta(q^13))/(eta(q)*eta(q^26)) )^2/q; Vec(A) \\ _G. C. Greubel_, Jun 14 2018

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

%Y Cf. A128518 (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 18 2014

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Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)