A058493 - OEIS

%I #21 Jun 14 2018 20:25:45

%S 1,4,0,-4,16,0,6,40,0,-8,96,0,17,204,0,-28,400,0,38,760,0,-56,1376,0,

%T 84,2404,0,-124,4096,0,172,6808,0,-232,11072,0,325,17688,0,-448,27792,

%U 0,594,43008,0,-784,65696,0,1049,99128,0

%N McKay-Thompson series of class 12e for Monster.

%C Agrees with A112149 except for signs.

%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="/A058493/b058493.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)/eta(q^6))^4 + 4*(eta(q^6)/eta(q^3))^4) in powers of q. - _G. A. Edgar_, Apr 17 2017

%e T12e = 1/q + 4*q - 4*q^5 + 16*q^7 + 6*q^11 + 40*q^13 - 8*q^17 + 96*q^19 + ...

%t eta[q_]:= q^(1/24)*QPochhammer[q]; b:= q^(1/2)*(eta[q^3]/eta[q^6])^4;

%t a:= CoefficientList[Series[b + 4*q/b, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 13 2018 *)

%o (PARI) q='q+O('q^60); A = (eta(q^3)/eta(q^6))^4; Vec(A + 4*q/A) \\ _G. C. Greubel_, Jun 13 2018

%Y Cf. A000521, A007240, A007263, A014708, A007241, A007267, A045478, A112149, etc.

%K sign

%O 0,2

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