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A058629 McKay-Thompson series of class 32A for Monster. 1

%I

%S 1,0,2,4,6,8,12,16,23,32,42,56,74,96,124,160,203,256,324,404,502,624,

%T 768,944,1156,1408,1710,2072,2500,3008,3612,4320,5157,6144,7296,8648,

%U 10232,12072,14220,16720,19616,22976,26868,31360,36546,42528,49404,57312

%N McKay-Thompson series of class 32A for Monster.

%H G. C. Greubel, <a href="/A058629/b058629.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, where A = (eta(q^2)*eta(q^16))^3/( eta(q)^2*eta(q^4) *eta(q^8)*eta(q^32)^2), in powers of q. - _G. C. Greubel_, Jun 23 2018

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

%e T32A = 1/q + 2*q + 4*q^2 + 6*q^3 + 8*q^4 + 12*q^5 + 16*q^6 + 23*q^7 + ...

%t eta[q_] := q^(1/24)*QPochhammer[q]; A := (eta[q^2]*eta[q^16])^3/( eta[q]^2*eta[q^4]*eta[q^8]*eta[q^32]^2); a:= CoefficientList[Series[ q*(-2 + 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^2)*eta(q^16))^3/( eta(q)^2*eta(q^4) *eta(q^8)*eta(q^32)^2)/q; Vec(A - 2) \\ _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 February 16 05:10 EST 2019. Contains 320140 sequences. (Running on oeis4.)