A130294 Degree of the n X n Brauer loop scheme. Also, the sum of components of the Brauer loop model in size n.

1, 1, 1, 3, 7, 55, 307, 6153, 82977, 4196961, 137460201, 17446527483, 1392263902567, 441865841817751, 86102618147479627, 68171466271082093265, 32487634563234662295169, 64060941478203660710291329, 74749048993664905589266454929, 366627599282115135074804792982963

Offset: 0

Author

Paul Zinn-Justin, Aug 06 2007

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..100
• A. Knutson and P. Zinn-Justin, A scheme related to the Brauer loop model, Adv. in Math. 214 (2007), 40-77.

Crossrefs

Cf. A130306.

Programs

Mathematica

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}]]];
Table[a[n], {n, 0, 19}] (* Jean-François Alcover, Dec 14 2018 *)

Formula

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.

Extensions

More terms from Alois P. Heinz, Dec 04 2018