A368022 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+4) with i,j = 0, ..., n-1.

1, 14, 3612, 14798454, 930744290905, 891107801867703108, 12977575456694246217097712, 2880177942851157900010279504962852, 9767068920318918290905853040035029840419305, 507521146153330160633968276251306280235282377512091202, 405202219609475677155580649938116235991326716758748940659564085180

Offset: 0

Author

Stefano Spezia, Dec 08 2023

Keywords

• nonn

Examples

			a(4) = 930744290905:
   14,   42,  132,   429;
   42,  132,  429,  1430;
  132,  429, 1430,  4862;
  429, 1430, 4862, 16796.
		

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, A006858.

Cf. A278843, A368012, A368019, A368021, A368023, A368024, A368025.

Column k=4 of A368026.

Programs

Mathematica

Join[{1},Table[Permanent[Table[CatalanNumber[i+j+4],{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+2))); \\ Michel Marcus, Dec 11 2023

Formula

Det(M(n)) = A006858(n+1).