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A368023 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+5) with i,j = 0, ..., n-1.

%I A368023 #16 Dec 23 2023 12:55:35
%S A368023 1,42,35442,499114473,111384708171022,386735380538157813864,
%T A368023 20749829798295730016646982120,17168067359133726591295713796489415774,
%U A368023 219043020447199737063468653002456184101044391781,43136143328071407602633546712654262446417322619276001391870
%N A368023 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+5) with i,j = 0, ..., n-1.
%H A368023 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 A368023 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 A368023 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%F A368023 Det(M(n)) = A091962(n+1).
%e A368023 a(4) = 111384708171022:
%e A368023     42,  132,   429,  1430;
%e A368023    132,  429,  1430,  4862;
%e A368023    429, 1430,  4862, 16796;
%e A368023   1430, 4862, 16796, 58786.
%t A368023 Join[{1},Table[Permanent[Table[CatalanNumber[i+j+5],{i,0,n-1},{j,0,n-1}]],{n,10}]]
%o A368023 (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
%o A368023 a(n) = matpermanent(matrix(n, n, i, j, C(i+j+3))); \\ _Michel Marcus_, Dec 11 2023
%Y A368023 Cf. A000108, A091962.
%Y A368023 Cf. A278843, A368012, A368019, A368021, A368022, A368024, A368025.
%Y A368023 Column k=5 of A368026.
%K A368023 nonn
%O A368023 0,2
%A A368023 _Stefano Spezia_, Dec 08 2023