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

0,4

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.

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.

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 *)

Crossrefs

Cf. A130306.

Sequence in context: A204254 A144030 A228490 * A321968 A100772 A320724

Adjacent sequences: A130291 A130292 A130293 * A130295 A130296 A130297

Keyword

nonn

Author

Paul Zinn-Justin, Aug 06 2007

Extensions

More terms from Alois P. Heinz, Dec 04 2018

Status

approved