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Degree of the n X n Brauer loop scheme. Also, the sum of components of the Brauer loop model in size n.
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%I #12 Dec 14 2018 06:31:27

%S 1,1,1,3,7,55,307,6153,82977,4196961,137460201,17446527483,

%T 1392263902567,441865841817751,86102618147479627,68171466271082093265,

%U 32487634563234662295169,64060941478203660710291329,74749048993664905589266454929,366627599282115135074804792982963

%N Degree of the n X n Brauer loop scheme. Also, the sum of components of the Brauer loop model in size n.

%H Alois P. Heinz, <a href="/A130294/b130294.txt">Table of n, a(n) for n = 0..100</a>

%H A. Knutson and P. Zinn-Justin, <a href="http://arXiv.org/abs/math.AG/0503224">A scheme related to the Brauer loop model</a>, Adv. in Math. 214 (2007), 40-77.

%F a(2n) = det(binomial(2i+2j+1,2i)), 0<=i,j<=n-1; a(2n+1) = det(binomial(2i+2j+3,2i+1)), 0<=i,j<=n-1.

%t a[n_] := Which[n == 0, 1, n == 1, 1, EvenQ[n], Det[Table[Binomial[2i + 2j + 1, 2i], {i, 0, n/2 - 1}, {j, 0, n/2 - 1}]], True, Det[Table[Binomial[2i + 2j + 3, 2i + 1], {i, 0, (n-1)/2 - 1}, {j, 0, (n-1)/2 - 1}]]];

%t Table[a[n], {n, 0, 19}] (* _Jean-François Alcover_, Dec 14 2018 *)

%Y Cf. A130306.

%K nonn

%O 0,4

%A _Paul Zinn-Justin_, Aug 06 2007

%E More terms from _Alois P. Heinz_, Dec 04 2018