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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.

%I A368298 #10 Dec 20 2023 19:06:09
%S A368298 1,1,53,490614,930744290905,386735380538157813864,
%T A368298 36494318768452684668237864399892,
%U A368298 800075179375382235705309991148469060609055210,4138855242465150993428071754285859188133806122546895149328625,5109461743591866972924602083859433690113667142460933537037028649653229023827000
%N 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.
%H A368298 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%e A368298 a(3) = 490614:
%e A368298    5,  14,  42;
%e A368298   14,  42, 132;
%e A368298   42, 132, 429.
%p A368298 with(LinearAlgebra):
%p A368298 C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
%p A368298 a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> C(i+j+n-2)))):
%p A368298 seq(a(n), n=0..10);  # _Alois P. Heinz_, Dec 20 2023
%t A368298 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 A368298 Cf. A000108, A355400.
%Y A368298 Diagonal of A368025.
%K A368298 nonn
%O A368298 0,3
%A A368298 _Stefano Spezia_, Dec 20 2023