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A320845 Permanent of the n X n symmetric Pascal matrix S(i, j) = A007318(i + j - 2, i - 2). 1
1, 3, 35, 1625, 301501, 223727931, 664027495067, 7882889445845553, 374307461786150039341, 71094317517818229430634443, 54016473080283197162871309369823, 164180413591614722725059485805374744105, 1996341102310530780023501278692058093020378765 (list; graph; refs; listen; history; text; internal format)
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

Cf. A007318, A006134.

Sequence in context: A136525 A136556 A006098 * A012499 A125530 A068726

Adjacent sequences:  A320842 A320843 A320844 * A320846 A320847 A320848

KEYWORD

nonn

AUTHOR

Stefano Spezia, Oct 22 2018

STATUS

approved

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Last modified April 21 20:59 EDT 2019. Contains 322328 sequences. (Running on oeis4.)