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%I #15 Aug 14 2020 11:50:03
%S 1,0,1,0,2,0,6,0,12,5,24,13,52,33,97,80,177,160,319,301,540,547,887,
%T 926,1429,1512,2219,2402,3367,3681,5015,5502,7294,8064,10419,11550,
%U 14664,16253,20287,22531,27682,30738,37319,41378,49671,55060,65390,72391,85250
%N Poincaré series for invariant polynomial functions on the space of binary forms of degree 10.
%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=10)
%e The Poincaré series is (1 - t^5 + 2t^6 - t^7 + 4t^8 + 4t^9 + 8t^10 + 6t^11 + 16t^12 + 9t^13 + 17t^14 + 15t^15 + 19t^16 + 12t^17 + 23t^18 + 12t^19 + 19t^20 + 15t^21 + 17t^22 + 9t^23 + 16t^24 + 6t^25 + 8t^26 + 4t^27 + 4t^28 - t^29 + 2t^30 - t^31 + t^36) / (1 - t^2)(1 - t^4)(1 - t^5)(1 - t^6)^2(1 - t^7)(1 - t^8)(1 - t^9)
%p nmax := 120 :
%p (1 - t^5 + 2*t^6 - t^7 + 4*t^8 + 4*t^9 + 8*t^10 + 6*t^11 + 16*t^12 + 9*t^13 + 17*t^14 + 15*t^15 + 19*t^16 + 12*t^17 + 23*t^18 + 12*t^19 + 19*t^20 + 15*t^21 + 17*t^22 + 9*t^23 + 16*t^24 + 6*t^25 + 8*t^26 + 4*t^27 + 4*t^28 - t^29 + 2*t^30 - t^31 + t^36) / (1 - t^2)/(1 - t^4)/(1 - t^5)/(1 - t^6)^2/(1 - t^7)/(1 - t^8)/(1 - t^9) ;
%p taylor(%,t=0,nmax) ;
%p gfun[seriestolist](%) ;
%p seq( %[1+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 0,5
%A _N. J. A. Sloane_, Oct 20 2017
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