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A368024 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+6) with i,j = 0, ..., n-1.

%I A368024 #16 Dec 23 2023 12:55:23
%S A368024 1,132,372801,18271508684,14570336513383508,184204867131613485842464,
%T A368024 36494318768452684668237864399892,
%U A368024 112700882376631374264115400599310944646268,5412697889621813132124427516447652973723355158580585,4039897382110972290799421201399595435416108353911344509968785100
%N A368024 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+6) with i,j = 0, ..., n-1.
%H A368024 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 A368024 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 A368024 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%e A368024 a(4) = 14570336513383508:
%e A368024    132,   429,  1430,   4862;
%e A368024    429,  1430,  4862,  16796;
%e A368024   1430,  4862, 16796,  58786;
%e A368024   4862, 16796, 58786, 208012.
%t A368024 Join[{1},Table[Permanent[Table[CatalanNumber[i+j+6],{i,0,n-1},{j,0,n-1}]],{n,9}]]
%o A368024 (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
%o A368024 a(n) = matpermanent(matrix(n, n, i, j, C(i+j+4))); \\ _Michel Marcus_, Dec 11 2023
%Y A368024 Cf. A000108, A335857 (determinant).
%Y A368024 Cf. A278843, A368012, A368019, A368021, A368022, A368023, A368025.
%Y A368024 Column k=6 of A368026.
%K A368024 nonn
%O A368024 0,2
%A A368024 _Stefano Spezia_, Dec 08 2023