A368021 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+3) with i,j = 0, ..., n-1.

1, 5, 406, 490614, 8755482505, 2318987094804471, 9179129956137993425772, 546580120389987275414413168012, 492460174883711250780962744103403975159, 6747075036368337341936435881321217868978170152215, 1411689504898999110533224343869931312130954127737962059963934

Offset: 0

Author

Stefano Spezia, Dec 08 2023

Keywords

• nonn

Examples

			a(4) = 8755482505:
    5,  14,  42,   132;
   14,  42, 132,   429;
   42, 132, 429,  1430;
  132, 429, 1430, 4862.
		

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, A000330, A355400.

Cf. A278843, A368012, A368019, A368022, A368023, A368024, A368025.

Column k=3 of A368026.

Programs

Mathematica

Join[{1},Table[Permanent[Table[CatalanNumber[i+j+3],{i,0,n-1},{j,0,n-1}]],{n,10}]]

PARI

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

Formula

Det(M(n)) = A000330(n+1) (see Mays and Wojciechowski, 2000).