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 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. 7
 1, 5, 406, 490614, 8755482505, 2318987094804471, 9179129956137993425772, 546580120389987275414413168012, 492460174883711250780962744103403975159, 6747075036368337341936435881321217868978170152215, 1411689504898999110533224343869931312130954127737962059963934 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Table of n, a(n) for n=0..10. Arthur T. Benjamin, Naiomi T. Cameron, Jennifer J. Quinn, and Carl R. Yerger, Catalan determinants-a combinatorial approach, Congressus Numerantium 200, 27-34 (2010).  On ResearchGate. M. E. Mays and Jerzy Wojciechowski, A determinant property of Catalan numbers. Discrete Math. 211, No. 1-3, 125-133 (2000). Wikipedia, Hankel matrix. FORMULA Det(M(n)) = A000330(n+1) (see Mays and Wojciechowski, 2000). EXAMPLE a(4) = 8755482505: 5, 14, 42, 132; 14, 42, 132, 429; 42, 132, 429, 1430; 132, 429, 1430, 4862. MATHEMATICA Join[{1}, Table[Permanent[Table[CatalanNumber[i+j+3], {i, 0, n-1}, {j, 0, n-1}]], {n, 10}]] PROG (PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108 a(n) = matpermanent(matrix(n, n, i, j, C(i+j+1))); \\ Michel Marcus, Dec 11 2023 CROSSREFS Cf. A000108, A000330, A355400. Cf. A278843, A368012, A368019, A368022, A368023, A368024, A368025. Column k=3 of A368026. Sequence in context: A198535 A128866 A221047 * A075769 A046274 A221700 Adjacent sequences: A368018 A368019 A368020 * A368022 A368023 A368024 KEYWORD nonn AUTHOR Stefano Spezia, Dec 08 2023 STATUS approved

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Last modified September 13 16:57 EDT 2024. Contains 375910 sequences. (Running on oeis4.)