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%I #29 Mar 15 2024 09:43:24
%S 1,2,6,14,29,56,107,186,320,530,851,1332,2051,3074,4544,6602,9444,
%T 13322,18579,25564,34827,46954,62692,82954,108889,141732,183169,
%U 235042,299584,379434,477763,598036,744628,922348,1136838,1394608,1703246,2071068,2508084
%N Expansion of o.g.f. (1-x^2+x^4)/((1-x)^2*(1-x^2)^4*(1-x^3)^4).
%C Poincaré series [or Poincare series] P(C_{3,2}; x).
%D B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331.
%H Peter J. C. Moses, <a href="/A123991/b123991.txt">Table of n, a(n) for n = 0..9999</a>
%H Dragomir Z. Djokovic, <a href="https://arxiv.org/abs/math/0609262">Poincaré series [or Poincare series] of some pure and mixed trace algebras of two generic matrices</a>. arXiv:math/0609262 [math.AC], 2006. See Table 3, lines 4 and 5, also Table 5, lines 1 and 2.
%H Y. Teranishi, <a href="https://projecteuclid.org/journals/nagoya-mathematical-journal/volume-104/issue-none/The-ring-of-invariants-of-matrices/nmj/1118780557.full">The ring of invariants of matrices</a>, Nagoya Math. J., 104 (1986), 149-161.
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (2, 3, -4, -10, 0, 24, 12, -27, -34, 11, 48, 11, -34, -27, 12, 24, 0, -10, -4, 3, 2, -1).
%F G.f.: (1+x^6)/((1-x)^2*(1-x^2)^3*(1-x^3)^4*(1-x^4)).
%t CoefficientList[Series[(1-x^2+x^4)/((1-x)^2(1-x^2)^4(1-x^3)^4),{x,0,40}],x] (* _Harvey P. Dale_, Dec 20 2014 *)
%Y Cf. A124636.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 21 2006