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A058671 McKay-Thompson series of class 42A for Monster. 1

%I

%S 1,0,2,2,3,2,9,6,11,14,18,16,31,30,46,50,66,66,106,102,146,160,204,

%T 216,297,306,401,448,552,594,777,816,1023,1134,1377,1492,1858,1998,

%U 2427,2684,3183,3488,4219,4566,5429,6000,7020,7688,9115,9918,11593,12806

%N McKay-Thompson series of class 42A for Monster.

%H G. C. Greubel, <a href="/A058671/b058671.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 David A. Madore, <a href="http://mathforum.org/kb/thread.jspa?forumID=253&amp;threadID=1602206&amp;messageID=5836094">Coefficients of Moonshine (McKay-Thompson) series</a>, The Math Forum

%H <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>

%F Expansion of A + 2 + 1/A, where A = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21) )/(eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2, in powers of q. - _G. C. Greubel_, Jun 24 2018

%F a(n) ~ exp(2*Pi*sqrt(2*n/21)) / (2^(3/4) * 21^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 27 2018

%e T42A = 1/q + 2*q + 2*q^2 + 3*q^3 + 2*q^4 + 9*q^5 + 6*q^6 + 11*q^7 + 14*q^8 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; A := ((eta[q]*eta[q^6]*eta[q^14]* eta[q^21])/(eta[q^2]*eta[q^3]*eta[q^7]*eta[q^42]))^2; a := CoefficientList[Series[2 + A + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 24 2018 *)

%o (PARI) q='q+O('q^50); A = ((eta(q)*eta(q^6)*eta(q^14)*eta(q^21))/( eta(q^2)*eta(q^3)*eta(q^7)*eta(q^42)))^2/q; Vec(A + 2 + 1/A) \\ _G. C. Greubel_, Jun 24 2018

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

%K nonn

%O -1,3

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

%E More terms from _Michel Marcus_, Feb 20 2014

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Last modified February 23 02:29 EST 2019. Contains 320411 sequences. (Running on oeis4.)