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%I #23 Nov 06 2018 17:50:35
%S 1,3,35,1625,301501,223727931,664027495067,7882889445845553,
%T 374307461786150039341,71094317517818229430634443,
%U 54016473080283197162871309369823,164180413591614722725059485805374744105,1996341102310530780023501278692058093020378765
%N Permanent of the n X n symmetric Pascal matrix S(i, j) = A007318(i + j - 2, i - 2).
%C The trace of the n X n symmetric Pascal matrix S is A006134(n).
%C The determinant of the n X n symmetric Pascal matrix S is equal to 1.
%H Vaclav Kotesovec, <a href="/A320845/b320845.txt">Table of n, a(n) for n = 1..26</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PascalMatrix.html">Pascal Matrix</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Pascal_matrix">Pascal matrix</a>
%e For n = 1 the matrix S is
%e 1
%e with the permanent equal to 1.
%e For n = 2 the matrix S is
%e 1, 1
%e 1, 2
%e with the permanent equal to 3.
%e For n = 3 the matrix S is
%e 1, 1, 1
%e 1, 2, 3
%e 1, 3, 6
%e with the permanent equal to 35.
%e For n = 4 the matrix S is
%e 1, 1, 1, 1
%e 1, 2, 3, 4
%e 1, 3, 6, 10
%e 1, 4, 10, 20
%e with the permanent equal to 1625.
%e ...
%p with(LinearAlgebra):
%p a := n -> Permanent(Matrix(n, (i, j) -> binomial(i+j-2, i-1))):
%p seq(a(n), n = 1 .. 15);
%t a[n_] := Permanent[Table[Binomial[i+j-2,i-1], {i, n}, {j, n}]]; Array[a, 15]
%o (PARI) a(n) = matpermanent(matrix(n, n, i, j, binomial(i+j-2, i-1))); \\ _Michel Marcus_, Nov 05 2018
%Y Cf. A007318, A006134.
%K nonn
%O 1,2
%A _Stefano Spezia_, Oct 22 2018
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