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%I #20 Oct 21 2022 22:02:18
%S 1,0,1,1,2,2,4,4,7,8,12,13,20,22,31,36,47,54,71,80,102,117,144,164,
%T 201,227,272,309,365,411,483,540,627,702,806,898,1026,1137,1289,1427,
%U 1606,1770,1985,2179,2429,2663,2952,3225,3565,3882,4272,4644,5090,5518,6032,6522
%N G.f.: (1+x^8+x^9+x^10+x^18)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)).
%C Poincare series for invariant polynomial functions on the space of binary forms of degree 8.
%H Andries Brouwer, <a href="http://www.win.tue.nl/~aeb/math/poincare.html">Poincaré Series</a> (See n=8).
%H J.-I. Igusa, <a href="https://www.jstor.org/stable/2373243">Modular forms and projective invariants</a>, Amer. J. Math., 89 (1967), 817-855; see p. 847.
%H Peter Littelmann and Claudio Procesi, <a href="https://doi.org/10.1016/0021-8693(90)90284-U">On the Poincaré series of the invariants of binary forms</a>, Journal of Algebra 133.2 (1990): 490-499. See last page.
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,3,3,0,-3,-4,-3,-1,1,2,3,3,2,1,-1,-3,-4,-3,0,3,3,1,-1,-1).
%o (PARI) Vec((1+x^8+x^9+x^10+x^18)/((1-x^2)*(1-x^3)*(1-x^4)*(1-x^5)*(1-x^6)*(1-x^7)) + O(x^50)) \\ _Jinyuan Wang_, Mar 10 2020
%Y For these Poincare 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.
%Y This Poincare series is mentioned in A079293.
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_, Sep 01 2004
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