A278843 a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = Catalan(i+j).

1, 2, 53, 19148, 97432285, 7146659536022, 7683122105385590481, 122557371932066196769721048, 29280740446653388021872592300048913, 105552099397122165176384278493772205485181002, 5775235099464970103806328103231969172586171168151193533

Offset: 0

Author

Vaclav Kotesovec, Nov 29 2016

Keywords

• nonn

Examples

			From _Stefano Spezia_, Dec 08 2023: (Start)
a(4) = 97432285:
   2,   5,  14,   42;
   5,  14,  42,  132;
  14,  42, 132,  429;
  42, 132, 429, 1430.
(End)
		

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, A277829, A278770, A278844.

Cf. A368012, A368019, A368021, A368022, A368023, A368024, A368025.

Column k=2 of A368026.

Programs

Mathematica

Flatten[{1, Table[Permanent[Table[CatalanNumber[i+j], {i, 1, n}, {j, 1, n}]], {n, 1, 14}]}]

PARI

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

Formula

Det(M(n)) = n + 1 (see Mays and Wojciechowski, 2000). - Stefano Spezia, Dec 08 2023