cp's OEIS Frontend

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

%I A320845 #24 Feb 16 2025 08:33:56
%S A320845 1,3,35,1625,301501,223727931,664027495067,7882889445845553,
%T A320845 374307461786150039341,71094317517818229430634443,
%U A320845 54016473080283197162871309369823,164180413591614722725059485805374744105,1996341102310530780023501278692058093020378765
%N A320845 Permanent of the n X n symmetric Pascal matrix S(i, j) = A007318(i + j - 2, i - 2).
%C A320845 The trace of the n X n symmetric Pascal matrix S is A006134(n).
%C A320845 The determinant of the n X n symmetric Pascal matrix S is equal to 1.
%H A320845 Vaclav Kotesovec, <a href="/A320845/b320845.txt">Table of n, a(n) for n = 1..26</a>
%H A320845 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PascalMatrix.html">Pascal Matrix</a>
%H A320845 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pascal_matrix">Pascal matrix</a>
%e A320845 For n = 1 the matrix S is
%e A320845    1
%e A320845 with the permanent equal to 1.
%e A320845 For n = 2 the matrix S is
%e A320845    1, 1
%e A320845    1, 2
%e A320845 with the permanent equal to 3.
%e A320845 For n = 3 the matrix S is
%e A320845    1, 1, 1
%e A320845    1, 2, 3
%e A320845    1, 3, 6
%e A320845 with the permanent equal to 35.
%e A320845 For n = 4 the matrix S is
%e A320845    1,  1,  1,   1
%e A320845    1,  2,  3,   4
%e A320845    1,  3,  6,  10
%e A320845    1,  4, 10,  20
%e A320845 with the permanent equal to 1625.
%e A320845 ...
%p A320845 with(LinearAlgebra):
%p A320845 a := n -> Permanent(Matrix(n, (i, j) -> binomial(i+j-2, i-1))):
%p A320845 seq(a(n), n = 1 .. 15);
%t A320845 a[n_] := Permanent[Table[Binomial[i+j-2,i-1], {i, n}, {j, n}]]; Array[a, 15]
%o A320845 (PARI) a(n) = matpermanent(matrix(n, n, i, j, binomial(i+j-2, i-1))); \\ _Michel Marcus_, Nov 05 2018
%Y A320845 Cf. A007318, A006134.
%K A320845 nonn
%O A320845 1,2
%A A320845 _Stefano Spezia_, Oct 22 2018