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A278843
a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = Catalan(i+j).
8
1, 2, 53, 19148, 97432285, 7146659536022, 7683122105385590481, 122557371932066196769721048, 29280740446653388021872592300048913, 105552099397122165176384278493772205485181002, 5775235099464970103806328103231969172586171168151193533
OFFSET
0,2
LINKS
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)) = n + 1 (see Mays and Wojciechowski, 2000). - Stefano Spezia, Dec 08 2023
EXAMPLE
From Stefano Spezia, Dec 08 2023: (Start)
a(4) = 97432285:
2, 5, 14, 42;
5, 14, 42, 132;
14, 42, 132, 429;
42, 132, 429, 1430.
(End)
MATHEMATICA
Flatten[{1, Table[Permanent[Table[CatalanNumber[i+j], {i, 1, n}, {j, 1, n}]], {n, 1, 14}]}]
PROG
(PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = matpermanent(matrix(n, n, i, j, C(i+j))); \\ Michel Marcus, Dec 11 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 29 2016
STATUS
approved