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%I #23 Jun 23 2018 14:16:43
%S 1,0,1,2,0,-2,3,0,1,6,0,-2,9,0,4,12,0,-2,18,0,1,26,0,-4,34,0,5,48,0,
%T -4,66,0,8,86,0,-12,115,0,12,152,0,-14,196,0,17,252,0,-16,324,0,17,
%U 410,0,-24,518,0,25,652,0,-28,815,0,42,1016,0,-50,1260,0,50,1556,0,-60,1914,0,74,2344,0
%N McKay-Thompson series of class 30b for Monster.
%H G. C. Greubel, <a href="/A058623/b058623.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 <a href="/index/Mat#McKay_Thompson">Index entries for McKay-Thompson series for Monster simple group</a>
%F Expansion of A + q^2/A, where A = q*(eta(q^6)*eta(q^15)/(eta(q^3) *eta(q^30)))^2, in powers of q. - _G. C. Greubel_, Jun 23 2018
%e T30b = 1/q + q + 2*q^2 - 2*q^4 + 3*q^5 + q^7 + 6*q^8 - 2*q^10 + 9*q^11 + ...
%t nmax = 80; QP = QPochhammer; A = x^2*O[x]^(nmax+1); A = (QP[x^3 + A] * (QP[x^30 + A]/QP[x^6 + A]/QP[x^15 + A]))^2*x; a[n_] := SeriesCoefficient[ 1/A + A, n]; Table[a[n], {n, -1, nmax}] (* _Jean-François Alcover_, Nov 14 2015, adapted from PARI *)
%t eta[q_]:= q^(1/24)*QPochhammer[q]; A := q*(eta[q^6]*eta[q^15]/(eta[q^3]* eta[q^30]))^2; a:= CoefficientList[Series[A + q^2/A, {q, 0, 60}], q]; Table[a[[n]], {n, 1, 50}] (* _G. C. Greubel_, Jun 23 2018 *)
%o (PARI) a(n)=local(A); if(n<-1,0, A=x^2*O(x^n); A=(eta(x^3+A)*eta(x^30+A)/eta(x^6+A)/eta(x^15+A))^2*x; polcoeff(1/A+A,n)) \\ _Michael Somos_, May 02 2004
%o (PARI) q='q+O('q^80); A = (eta(q^6)*eta(q^15)/(eta(q^3) *eta(q^30)))^2; Vec(A+ q^2/A) \\ _G. C. Greubel_, Jun 23 2018
%Y Cf. A000521, A007240, A014708, A007241, A007267, A045478, etc.
%K sign
%O -1,4
%A _N. J. A. Sloane_, Nov 27 2000
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