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

0,2

Links

Table of n, a(n) for n=0..9.

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.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000108, A335857 (determinant).

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

Column k=6 of A368026.

Sequence in context: A289294 A321975 A289568 * A114534 A147692 A028674

Adjacent sequences: A368021 A368022 A368023 * A368025 A368026 A368027

Keyword

nonn

Author

Stefano Spezia, Dec 08 2023

Status

approved