A368019 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+1) with i,j = 0, ..., n-1.

1, 1, 9, 979, 1417675, 28665184527, 8325587326635565, 35389363346700690999467, 2230867495754739989535874468003, 2106171270085074740753132799048111935155, 30007898337707083458776293190436074888346472515407, 6491219550166075876771081259839537013093735814742318424677245

Offset

0,3

Links

Table of n, a(n) for n=0..11.

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

Cf. A000108.

Cf. A278843, A368012, A368021, A368022, A368023, A368024, A368025.

Column k=1 of A368026.

Sequence in context: A087590 A048561 A361885 * A112909 A083909 A307324

Adjacent sequences: A368016 A368017 A368018 * A368020 A368021 A368022

Keyword

nonn

Author

Stefano Spezia, Dec 08 2023

Status

approved