%I #21 Jun 04 2018 09:23:11
%S 1,0,-3,2,0,6,5,0,3,6,0,-18,12,0,21,16,0,6,27,0,-60,34,0,72,51,0,24,
%T 70,0,-168,101,0,183,134,0,54,182,0,-411,240,0,450,322,0,138,416,0,
%U -936,544,0,981,696,0,282,902,0,-1989,1144,0,2070,1462,0,597,1832
%N McKay-Thompson series of class 9d for Monster.
%H G. C. Greubel, <a href="/A058096/b058096.txt">Table of n, a(n) for n = -1..5000</a> (terms -1..997 from G. A. Edgar)
%H D. Ford, J. McKay and S. P. Norton, <a href="http://dx.doi.org/10.1080/00927879408825127">More on replicable functions</a>, Comm. 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 G.f. is a period 1 Fourier series which satisfies f(-1 / (81 t)) = f(t) where q = exp(2 Pi i t). - _Michael Somos_, Aug 28 2015
%F a(3*n - 1) = A058601(n). a(3*n) = 0. a(3*n + 1) = -3 * A192309(n). - _Michael Somos_, Aug 28 2015
%F Expansion of A - 3/A, where A = (eta(q^9)^2/(eta(q^3)*eta(q^27)))^2, in powers of q. - _G. C. Greubel_, Jun 03 2018
%e T9d = 1/q - 3*q + 2*q^2 + 6*q^4 + 5*q^5 + 3*q^7 + 6*q^8 - 18*q^10 + 12*q^11 + ...
%t a[ n_] := With[ {A = 1/q (QPochhammer[ q^9]^2 / (QPochhammer[ q^3] QPochhammer[ q^27]))^2}, seriesCoefficient[ A - 3 / A, {q, 0, n}]]; (* _Michael Somos_, Aug 28 2015 *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A := (eta[q^9]^2/(eta[q^3]*eta[q^27]) )^2; a := CoefficientList[Series[q*(A - 3/A), {q, 0, 60}], q];
%t Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 03 2018 *)
%o (PARI) {a(n) = my(A); if( n<-1, 0, n++; A = x * O(x^n); A = eta(x^9 + A)^4 / (eta(x^3 + A) * eta(x^27 + A))^2; polcoeff( A - 3 * x^2 / A, n))}; /* _Michael Somos_, Aug 28 2015 */
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A058601, A192309.
%K sign
%O -1,3
%A _N. J. A. Sloane_, Nov 27 2000