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%I #14 Aug 14 2020 11:49:49
%S 1,0,2,0,13,13,73,110,320,529,1160,1893,3569,5633,9600,14636,23246,
%T 34233,51618,73716,106678,148325,207652,281963,384141,510882,680155,
%U 888201,1159414,1489689,1911698,2421067,3060774,3826640,4774174,5899837,7274612,8895981,10853618,13146996
%N Poincaré series for invariant polynomial functions on the space of binary forms of degree 11.
%C Many of these Poincaré series has every other term zero, in which case these zeros have been omitted.
%H Andries Brouwer, <a href="http://www.win.tue.nl/~aeb/math/poincare.html">Poincaré Series</a> (See n=11)
%e The Poincaré series is (1 + t^4 - t^6 + 10t^8 + 11t^10 + 58t^12 + 85t^14 + 222t^16 + 336t^18 + 660t^20 + 951t^22 + 1589t^24 + 2154t^26 + 3188t^28 + 4080t^30 + 5510t^32 + 6633t^34 + 8310t^36 + 9443t^38 + 11059t^40 + 11894t^42 + 13094t^44 + 13319t^46 + 13852t^48 + 13319t^50 + 13094t^52 + 11894t^54 + 11059t^56 + 9443t^58 + 8310t^60 + 6633t^62 + 5510t^64 + 4080t^66 + 3188t^68 + 2154t^70 + 1589t^72 + 951t^74 + 660t^76 + 336t^78 + 222t^80 + 85t^82 + 58t^84 + 11t^86 + 10t^88 - t^90 + t^92 + t^96) / (1 - t^4)(1 - t^6)(1 - t^8)(1 - t^10)(1 - t^12)(1 - t^14)(1 - t^16)(1 - t^18)(1 - t^20)
%p nmax := 120 :
%p (1 + t^4 - t^6 + 10*t^8 + 11*t^10 + 58*t^12 + 85*t^14 + 222*t^16 + 336*t^18 + 660*t^20 + 951*t^22 + 1589*t^24 + 2154*t^26 + 3188*t^28 + 4080*t^30 + 5510*t^32 + 6633*t^34 + 8310*t^36 + 9443*t^38 + 11059*t^40 + 11894*t^42 + 13094*t^44 + 13319*t^46 + 13852*t^48 + 13319*t^50 + 13094*t^52 + 11894*t^54 + 11059*t^56 + 9443*t^58 + 8310*t^60 + 6633*t^62 + 5510*t^64 + 4080*t^66 + 3188*t^68 + 2154*t^70 + 1589*t^72 + 951*t^74 + 660*t^76 + 336*t^78 + 222*t^80 + 85*t^82 + 58*t^84 + 11*t^86 + 10*t^88 - t^90 + t^92 + t^96) / (1 - t^4)/(1 - t^6)/(1 - t^8)/(1 - t^10)/(1 - t^12)/(1 - t^14)/(1 - t^16)/(1 - t^18)/(1 - t^20) ;
%p taylor(%,t=0,nmax) ;
%p gfun[seriestolist](%) ;
%p seq( %[1+2*i],i=0..nmax/2-1) ; # _R. J. Mathar_, Oct 26 2017
%Y For these Poincaré series for d = 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 24 see A097852, A293933, A097851, A293934, A293935, A293936, A293937, A293938, A293939, A293940, A293941, A293942, A293943 respectively.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Oct 20 2017
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