OFFSET
0,3
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)) = 1 (see Mays and Wojciechowski, 2000).
EXAMPLE
a(4) = 1417675:
1, 2, 5, 14;
2, 5, 14, 42;
5, 14, 42, 132;
14, 42, 132, 429.
MATHEMATICA
Join[{1}, Table[Permanent[Table[CatalanNumber[i+j+1], {i, 0, n-1}, {j, 0, n-1}]], {n, 11}]]
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 09 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Dec 08 2023
STATUS
approved