A278843 - OEIS

%I #8 Dec 23 2023 12:56:27

%S 1,2,53,19148,97432285,7146659536022,7683122105385590481,

%T 122557371932066196769721048,29280740446653388021872592300048913,

%U 105552099397122165176384278493772205485181002,5775235099464970103806328103231969172586171168151193533

%N a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = Catalan(i+j).

%H 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 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.

%F Det(M(n)) = n + 1 (see Mays and Wojciechowski, 2000). - _Stefano Spezia_, Dec 08 2023

%e From _Stefano Spezia_, Dec 08 2023: (Start)

%e a(4) = 97432285:

%e    2,   5,  14,   42;

%e    5,  14,  42,  132;

%e   14,  42, 132,  429;

%e   42, 132, 429, 1430.

%e (End)

%t Flatten[{1, Table[Permanent[Table[CatalanNumber[i+j], {i, 1, n}, {j, 1, n}]], {n, 1, 14}]}]

%o (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108

%o a(n) = matpermanent(matrix(n, n, i, j, C(i+j))); \\ _Michel Marcus_, Dec 11 2023

%Y Cf. A000108, A277829, A278770, A278844.

%Y Cf. A368012, A368019, A368021, A368022, A368023, A368024, A368025.

%Y Column k=2 of A368026.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Nov 29 2016