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A368026 Array read by ascending antidiagonals: A(n, k) 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+k) with i,j = 0, ..., n-1.

%I A368026 #18 Dec 23 2023 12:55:49
%S A368026 1,1,1,3,1,1,95,9,2,1,38057,979,53,5,1,207372681,1417675,19148,406,14,
%T A368026 1,15977248385955,28665184527,97432285,490614,3612,42,1,
%U A368026 17828166968924572623,8325587326635565,7146659536022,8755482505,14798454,35442,132,1,292842668371666277607183121,35389363346700690999467,7683122105385590481,2318987094804471,930744290905,499114473,372801,429,1
%N A368026 Array read by ascending antidiagonals: A(n, k) 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+k) with i,j = 0, ..., n-1.
%H A368026 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%e A368026 The array begins:
%e A368026       1,       1,        1,          1,            1, ...
%e A368026       1,       1,        2,          5,           14, ...
%e A368026       3,       9,       53,        406,         3612, ...
%e A368026      95,     979,    19148,     490614,     14798454, ...
%e A368026   38057, 1417675, 97432285, 8755482505, 930744290905, ...
%e A368026   ...
%p A368026 with(LinearAlgebra):
%p A368026 C:= proc(n) option remember; binomial(2*n, n)/(n+1) end:
%p A368026 A:= (n, k)-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> C(i+j+k-2)))):
%p A368026 seq(seq(A(d-k, k), k=0..d), d=0..8);  # _Alois P. Heinz_, Dec 20 2023
%t A368026 A[n_,k_]:=If[n==0,1,Permanent[Table[CatalanNumber[i+j+k],{i,0,n-1},{j,0,n-1}]]]; Table[A[n-k,k],{n,0,8},{k,0,n}]//Flatten
%Y A368026 Cf. A000012 (n=0), A000108 (n=1).
%Y A368026 Cf. A368012 (k=0), A368019 (k=1), A278843 (k=2), A368021 (k=3), A368022 (k=4), A368023 (k=5), A368024 (k=6).
%Y A368026 Cf. A368025 (determinant), A368298 (diagonal).
%K A368026 nonn,tabl
%O A368026 0,4
%A A368026 _Stefano Spezia_, Dec 08 2023