A368298 - OEIS

%I #10 Dec 20 2023 19:06:09

%S 1,1,53,490614,930744290905,386735380538157813864,

%T 36494318768452684668237864399892,

%U 800075179375382235705309991148469060609055210,4138855242465150993428071754285859188133806122546895149328625,5109461743591866972924602083859433690113667142460933537037028649653229023827000

%N 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.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.

%e a(3) = 490614:

%e    5,  14,  42;

%e   14,  42, 132;

%e   42, 132, 429.

%p with(LinearAlgebra):

%p C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:

%p a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> C(i+j+n-2)))):

%p seq(a(n), n=0..10);  # _Alois P. Heinz_, Dec 20 2023

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

%Y Cf. A000108, A355400.

%Y Diagonal of A368025.

%K nonn

%O 0,3

%A _Stefano Spezia_, Dec 20 2023