A368298 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+n) with i,j = 0, ..., n-1.

1, 1, 53, 490614, 930744290905, 386735380538157813864, 36494318768452684668237864399892, 800075179375382235705309991148469060609055210, 4138855242465150993428071754285859188133806122546895149328625, 5109461743591866972924602083859433690113667142460933537037028649653229023827000

Offset: 0

Author

Stefano Spezia, Dec 20 2023

Keywords

• nonn

Examples

			a(3) = 490614:
   5,  14,  42;
  14,  42, 132;
  42, 132, 429.
		

Links

• Wikipedia, Hankel matrix.

Crossrefs

Cf. A000108, A355400.

Diagonal of A368025.

Programs

Maple

with(LinearAlgebra):
C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> C(i+j+n-2)))):
seq(a(n), n=0..10);  # Alois P. Heinz, Dec 20 2023

Mathematica

a[n_]:=If[n==0, 1, Permanent[Table[CatalanNumber[i+j+n], {i, 0, n-1}, {j, 0, n-1}]]]; Array[a,10,0]