A278843 a(n) = permanent M_n where M_n is the n X n matrix m(i,j) = Catalan(i+j).

1, 2, 53, 19148, 97432285, 7146659536022, 7683122105385590481, 122557371932066196769721048, 29280740446653388021872592300048913, 105552099397122165176384278493772205485181002, 5775235099464970103806328103231969172586171168151193533

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)) = 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

Cf. A000108, A277829, A278770, A278844.

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

Column k=2 of A368026.

Sequence in context: A265443 A234603 A087865 * A083471 A078691 A280754

Adjacent sequences: A278840 A278841 A278842 * A278844 A278845 A278846

Keyword

nonn

Author

Vaclav Kotesovec, Nov 29 2016

Status

approved