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A368022 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+4) with i,j = 0, ..., n-1.

%I A368022 #16 Dec 23 2023 12:38:15
%S A368022 1,14,3612,14798454,930744290905,891107801867703108,
%T A368022 12977575456694246217097712,2880177942851157900010279504962852,
%U A368022 9767068920318918290905853040035029840419305,507521146153330160633968276251306280235282377512091202,405202219609475677155580649938116235991326716758748940659564085180
%N A368022 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+4) with i,j = 0, ..., n-1.
%H A368022 Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn, and Carl R. Yerger, <a href="https://combinatorialpress.com/cn/arch/vol200/">Catalan determinants-a combinatorial approach</a>, Congressus Numerantium 200, 27-34 (2010).  <a href="https://www.researchgate.net/publication/249812385_Catalan_determinants-a_combinatorial_approach">On ResearchGate</a>.
%H A368022 M. E. Mays and Jerzy Wojciechowski, <a href="https://doi.org/10.1016/S0012-365X(99)00140-5">A determinant property of Catalan numbers</a>. Discrete Math. 211, No. 1-3, 125-133 (2000).
%H A368022 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%F A368022 Det(M(n)) = A006858(n+1).
%e A368022 a(4) = 930744290905:
%e A368022    14,   42,  132,   429;
%e A368022    42,  132,  429,  1430;
%e A368022   132,  429, 1430,  4862;
%e A368022   429, 1430, 4862, 16796.
%t A368022 Join[{1},Table[Permanent[Table[CatalanNumber[i+j+4],{i,0,n-1},{j,0,n-1}]],{n,10}]]
%o A368022 (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
%o A368022 a(n) = matpermanent(matrix(n, n, i, j, C(i+j+2))); \\ _Michel Marcus_, Dec 11 2023
%Y A368022 Cf. A000108, A006858.
%Y A368022 Cf. A278843, A368012, A368019, A368021, A368023, A368024, A368025.
%Y A368022 Column k=4 of A368026.
%K A368022 nonn
%O A368022 0,2
%A A368022 _Stefano Spezia_, Dec 08 2023