cp's OEIS Frontend

A368021 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+3) with i,j = 0, ..., n-1.

%I A368021 #17 Dec 23 2023 12:38:06
%S A368021 1,5,406,490614,8755482505,2318987094804471,9179129956137993425772,
%T A368021 546580120389987275414413168012,
%U A368021 492460174883711250780962744103403975159,6747075036368337341936435881321217868978170152215,1411689504898999110533224343869931312130954127737962059963934
%N A368021 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+3) with i,j = 0, ..., n-1.
%H A368021 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 A368021 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 A368021 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>.
%F A368021 Det(M(n)) = A000330(n+1) (see Mays and Wojciechowski, 2000).
%e A368021 a(4) = 8755482505:
%e A368021     5,  14,  42,   132;
%e A368021    14,  42, 132,   429;
%e A368021    42, 132, 429,  1430;
%e A368021   132, 429, 1430, 4862.
%t A368021 Join[{1},Table[Permanent[Table[CatalanNumber[i+j+3],{i,0,n-1},{j,0,n-1}]],{n,10}]]
%o A368021 (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
%o A368021 a(n) = matpermanent(matrix(n, n, i, j, C(i+j+1))); \\ _Michel Marcus_, Dec 11 2023
%Y A368021 Cf. A000108, A000330, A355400.
%Y A368021 Cf. A278843, A368012, A368019, A368022, A368023, A368024, A368025.
%Y A368021 Column k=3 of A368026.
%K A368021 nonn
%O A368021 0,2
%A A368021 _Stefano Spezia_, Dec 08 2023