|
|
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.
|
|
7
|
|
|
1, 1, 9, 979, 1417675, 28665184527, 8325587326635565, 35389363346700690999467, 2230867495754739989535874468003, 2106171270085074740753132799048111935155, 30007898337707083458776293190436074888346472515407, 6491219550166075876771081259839537013093735814742318424677245
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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
|
|
|
STATUS
|
approved
|
|
|
|