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%I #20 Jun 16 2018 18:32:10
%S 1,-4,0,-4,-16,0,6,-40,0,-8,-96,0,17,-204,0,-28,-400,0,38,-760,0,-56,
%T -1376,0,84,-2404,0,-124,-4096,0,172,-6808,0,-232,-11072,0,325,-17688,
%U 0,-448,-27792,0,594,-43008,0,-784,-65696,0,1049,-99128,0,-1388,-147888,0,1796,-218408,0,-2320
%N McKay-Thompson series of class 12f for the Monster group.
%C The convolution square of this sequence is A007263 except for the constant term: T12e(q)^2 = T6d(q^2) - 8. - _G. A. Edgar_, Apr 17 2017
%H G. C. Greubel, <a href="/A112149/b112149.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..503 from G. A. Edgar)
%H D. Alexander, C. Cummins, J. McKay and C. Simons, <a href="http://oeis.org/A007242/a007242_1.pdf">Completely Replicable Functions</a>, LMS Lecture Notes, 165, ed. Liebeck and Saxl (1992), 87-98, annotated and scanned copy.
%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 q^(1/2) * (eta(q^3)^4/eta(q^6)^4 - 4*eta(q^6)^4/eta(q^3)^4) in powers of q. - _G. A. Edgar_, Apr 17 2017
%e T12f = 1/q -4*q -4*q^5 -16*q^7 +6*q^11 -40*q^13 -8*q^17 +...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a[n_]:= SeriesCoefficient[q^(1/2)* (eta[q^3]^4/eta[q^6]^4 - 4*eta[q^6]^4/eta[q^3]^4), {q, 0, n}]; Table[a[n], {n,0,50}] (* _G. C. Greubel_, Jan 25 2018 *)
%o (PARI) q='q+O('q^50); A = (eta(q^3)/eta(q^6))^4; Vec(A - 4*q/A) \\ _G. C. Greubel_, Jun 16 2018
%Y Cf. A007263, A058493, etc.
%K sign
%O 0,2
%A _Michael Somos_, Aug 28 2005
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