OFFSET
1,2
COMMENTS
The trace of the n X n symmetric Pascal matrix S is A006134(n).
The determinant of the n X n symmetric Pascal matrix S is equal to 1.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..26
Eric Weisstein's World of Mathematics, Pascal Matrix
Wikipedia, Pascal matrix
EXAMPLE
For n = 1 the matrix S is
1
with the permanent equal to 1.
For n = 2 the matrix S is
1, 1
1, 2
with the permanent equal to 3.
For n = 3 the matrix S is
1, 1, 1
1, 2, 3
1, 3, 6
with the permanent equal to 35.
For n = 4 the matrix S is
1, 1, 1, 1
1, 2, 3, 4
1, 3, 6, 10
1, 4, 10, 20
with the permanent equal to 1625.
...
MAPLE
with(LinearAlgebra):
a := n -> Permanent(Matrix(n, (i, j) -> binomial(i+j-2, i-1))):
seq(a(n), n = 1 .. 15);
MATHEMATICA
a[n_] := Permanent[Table[Binomial[i+j-2, i-1], {i, n}, {j, n}]]; Array[a, 15]
PROG
(PARI) a(n) = matpermanent(matrix(n, n, i, j, binomial(i+j-2, i-1))); \\ Michel Marcus, Nov 05 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Stefano Spezia, Oct 22 2018
STATUS
approved