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%I #22 Apr 23 2022 13:53:31
%S 1,1,4,6,14,23,45,72,126,195,315,472,720,1042,1520,2132,2995,4089,
%T 5568,7418,9843,12833,16652,21304,27117,34114,42705,52930,65294,79867,
%U 97253,117562,141516,169265,201665,238922,282030,331264,387780,451920,525023,607517
%N Molien series for group Gamma_{3,0}(2).
%H Bernhard Runge, <a href="http://projecteuclid.org/euclid.nmj/1118775400">On Siegel modular forms, part II</a>, Nagoya Math. J. 138, 179-197 (1995)
%H <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -3, -1, 1, 4, -2, -5, 3, 4, 0, -4, -3, 5, 2, -4, -1, 1, 3, -1, -2, 1).
%F G.f.: N_Hecke(x)*(1 + x^2)/((1 - x^2)*(1 - x^4)^3*(1 - x^6)*(1 - x^12)*(1 - x^14)) where N_Hecke(x)= 1 - x^2 + x^4 + 2*x^8 + x^10 + 2*x^12 + x^14 + 5*x^16 + x^18 + 6*x^20 + 2*x^22 + 6*x^24 + 2*x^26 + 6*x^28 + x^30 + 5*x^32 + x^34 + 2*x^36 + x^38 + 2*x^40 + x^44 - x^46 + x^48.
%t CoefficientList[Series[-(1-x+x^2+2 x^4+x^5+2 x^6+x^7+5 x^8+x^9+6 x^10+2 x^11+6 x^12+2 x^13+6 x^14+x^15+5 x^16+x^17+2 x^18+x^19+2 x^20+x^22-x^23+x^24)/((-1+x)^7 (1+x)^3 (1-x+x^2) (1+x+x^2)^2 (1+x+x^2+x^3+x^4+x^5+x^6)),{x,0,30}],x] (* _Peter J. C. Moses_, Dec 22 2013 *)
%t LinearRecurrence[{2,1,-3,-1,1,4,-2,-5,3,4,0,-4,-3,5,2,-4,-1,1,3,-1,-2,1},{1,1,4,6,14,23,45,72,126,195,315,472,720,1042,1520,2132,2995,4089,5568,7418,9843,12833,16652,21304,27117},50] (* _Harvey P. Dale_, Apr 23 2022 *)
%K nonn,easy,nice
%O 0,3
%A _N. J. A. Sloane_
%E More terms and formula from Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 24 2001
%E More terms from _Peter J. C. Moses_, Dec 22 2013
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