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A058606 McKay-Thompson series of class 28A for Monster. 1

%I #24 Jun 28 2018 04:39:38

%S 1,3,1,7,7,18,18,35,38,65,71,119,140,207,240,356,409,581,679,946,1100,

%T 1493,1738,2307,2704,3528,4134,5314,6221,7907,9233,11613,13566,16907,

%U 19700,24336,28350,34716,40379,49140,57090,68991,80021,96188,111357,133156,153923,183194,211422

%N McKay-Thompson series of class 28A for Monster.

%H G. C. Greubel, <a href="/A058606/b058606.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 + q/A, where A = q^(1/2)*((eta(q^2)*eta(q^7))/(eta(q) *eta(q^14)))^2, in powers of q. - _G. C. Greubel_, Jun 18 2018

%F a(n) ~ exp(2*Pi*sqrt(n/7)) / (2 * 7^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 28 2018

%e T28A = 1/q + 3*q + q^3 + 7*q^5 + 7*q^7 + 18*q^9 + 18*q^11 + 35*q^13 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; e28D:= q^(1/2)*((eta[q^2]*eta[q^7])/(eta[q]*eta[q^14]))^2; a[n_]:= SeriesCoefficient[e28D + q/e28D, {q, 0, n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Feb 18 2018 *)

%o (PARI) q='q+O('q^50); A = ((eta(q^2)*eta(q^7))/(eta(q) *eta(q^14)))^2; Vec(A + q/A) \\ _G. C. Greubel_, Jun 18 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_, Feb 18 2018

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Last modified March 29 04:59 EDT 2024. Contains 371264 sequences. (Running on oeis4.)