A368024 a(n) is the permanent of the n-th order Hankel matrix of Catalan numbers M(n) whose generic element is given by M(i,j) = A000108(i+j+6) with i,j = 0, ..., n-1.

1, 132, 372801, 18271508684, 14570336513383508, 184204867131613485842464, 36494318768452684668237864399892, 112700882376631374264115400599310944646268, 5412697889621813132124427516447652973723355158580585, 4039897382110972290799421201399595435416108353911344509968785100

Offset: 0

Author

Stefano Spezia, Dec 08 2023

Keywords

• nonn

Examples

			a(4) = 14570336513383508:
   132,   429,  1430,   4862;
   429,  1430,  4862,  16796;
  1430,  4862, 16796,  58786;
  4862, 16796, 58786, 208012.
		

Links

• Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn, and Carl R. Yerger, Catalan determinants-a combinatorial approach, Congressus Numerantium 200, 27-34 (2010). On ResearchGate.
• M. E. Mays and Jerzy Wojciechowski, A determinant property of Catalan numbers. Discrete Math. 211, No. 1-3, 125-133 (2000).
• Wikipedia, Hankel matrix.

Crossrefs

Cf. A000108, A335857 (determinant).

Cf. A278843, A368012, A368019, A368021, A368022, A368023, A368025.

Column k=6 of A368026.

Programs

Mathematica

Join[{1},Table[Permanent[Table[CatalanNumber[i+j+6],{i,0,n-1},{j,0,n-1}]],{n,9}]]

PARI

C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = matpermanent(matrix(n, n, i, j, C(i+j+4))); \\ Michel Marcus, Dec 11 2023