%I #32 Jun 14 2018 20:25:58
%S 1,0,0,-2,2,-2,3,-2,5,-6,5,-6,9,-10,10,-16,17,-18,25,-26,31,-38,37,
%T -48,60,-62,68,-84,95,-104,125,-134,154,-182,192,-220,257,-274,309,
%U -360,394,-434,492,-544,607,-688,740,-824,944,-1018,1123,-1266,1377,-1524,1697,-1850,2041,-2264,2461,-2708
%N McKay-Thompson series of class 30C for Monster.
%H Seiichi Manyama, <a href="/A058614/b058614.txt">Table of n, a(n) for n = -1..10000</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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F G.f.: u + v - 1 = u * v + 1 where u = Product_{k>0} (1 - x^k) * (1 - x^(15*k)) / ((1 - x^(6*k)) * (1 - x^(10*k))), v = 1/x * Product_{k>0} (1 - x^(3*k)) * (1 - x^(5*k)) / ((1 - x^(2*k)) * (1 - x^(30*k))). - _Seiichi Manyama_, May 04 2017
%F a(n) ~ -(-1)^n * exp(2*Pi*sqrt(n/15)) / (2*15^(1/4)*n^(3/4)). - _Vaclav Kotesovec_, Jun 06 2018
%F Expansion of 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/(eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30)) in powers of q. - _G. C. Greubel_, Jun 14 2018
%e T30C = 1/q - 2*q^2 + 2*q^3 - 2*q^4 + 3*q^5 - 2*q^6 + 5*q^7 - 6*q^8 + ...
%t eta[q_]:= q^(1/24)*QPochhammer[q]; a:= CoefficientList[Series[q*(1 + eta[q]*eta[q^3]*eta[q^5]*eta[q^15]/(eta[q^2]*eta[q^6]* eta[q^10]* eta[q^30])), {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)
%t QP=QPochhammer; a:= CoefficientList[Series[q + QP[q]*QP[q^3]*QP[q^5]* QP[q^15]/(QP[q^2]*QP[q^6]*QP[q^10]*QP[q^30]), {q,0,60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 14 2018 *)
%o (PARI) q='q+O('q^50); A = 1 + eta(q)*eta(q^3)*eta(q^5)*eta(q^15)/( eta(q^2)*eta(q^6)* eta(q^10)*eta(q^30))/q; Vec(A) \\ _G. C. Greubel_, Jun 14 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%Y Cf. A132321 (same sequence except for n=0).
%Y Cf. A131797 (u), A058618 (v).
%K sign
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
%E More terms from _Michel Marcus_, Feb 18 2014