A278843 - OEIS

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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).

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

(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)) = 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)