A368023 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+5) with i,j = 0, ..., n-1.

1, 42, 35442, 499114473, 111384708171022, 386735380538157813864, 20749829798295730016646982120, 17168067359133726591295713796489415774, 219043020447199737063468653002456184101044391781, 43136143328071407602633546712654262446417322619276001391870

Offset: 0

Author

Stefano Spezia, Dec 08 2023

Keywords

• nonn

Examples

			a(4) = 111384708171022:
    42,  132,   429,  1430;
   132,  429,  1430,  4862;
   429, 1430,  4862, 16796;
  1430, 4862, 16796, 58786.
		

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, A091962.

Cf. A278843, A368012, A368019, A368021, A368022, A368024, A368025.

Column k=5 of A368026.

Programs

Mathematica

Join[{1},Table[Permanent[Table[CatalanNumber[i+j+5],{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+3))); \\ Michel Marcus, Dec 11 2023

Formula

Det(M(n)) = A091962(n+1).