A320845 Permanent of the n X n symmetric Pascal matrix S(i, j) = A007318(i + j - 2, i - 2).

1, 3, 35, 1625, 301501, 223727931, 664027495067, 7882889445845553, 374307461786150039341, 71094317517818229430634443, 54016473080283197162871309369823, 164180413591614722725059485805374744105, 1996341102310530780023501278692058093020378765

Offset: 1

Author

Stefano Spezia, Oct 22 2018

Keywords

• nonn

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.

Examples

			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.
...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..26
• Eric Weisstein's World of Mathematics, Pascal Matrix
• Wikipedia, Pascal matrix

Crossrefs

Cf. A007318, A006134.

Programs

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]

PARI

a(n) = matpermanent(matrix(n, n, i, j, binomial(i+j-2, i-1))); \\ Michel Marcus, Nov 05 2018