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A058659 McKay-Thompson series of class 39A for Monster. 2

%I

%S 1,0,3,1,3,6,6,9,15,15,21,30,34,42,60,66,84,108,127,153,201,226,276,

%T 342,400,471,585,667,795,954,1103,1290,1551,1771,2073,2442,2807,3246,

%U 3816,4346,5028,5838,6662,7638,8856,10040,11505,13212,14991,17064,19560

%N McKay-Thompson series of class 39A for Monster.

%H G. C. Greubel, <a href="/A058659/b058659.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 - 1 + 1/A, where A = (eta(q^3)*eta(q^13)/(eta(q)* eta(q^39))), in powers of q. - _G. C. Greubel_, Jun 23 2018

%F a(n) ~ exp(4*Pi*sqrt(n/39)) / (sqrt(2) * 39^(1/4) * n^(3/4)). - _Vaclav Kotesovec_, Jun 27 2018

%e T39A = 1/q + 3*q + q^2 + 3*q^3 + 6*q^4 + 6*q^5 + 9*q^6 + 15*q^7 + 15*q^8 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A:= (eta[q^3]*eta[q^13]/( eta[q]* eta[q^39])); a := CoefficientList[Series[A - 1 + 1/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 23 2018 *)

%o (PARI) q='q+O('q^50); A = eta(q^3)*eta(q^13)/(q*eta(q)*eta(q^39)); Vec(A - 1 +1/A) \\ _G. C. Greubel_, Jun 23 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 July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)