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Determinant of the adjacency matrix of the n-cube graph Q_n.
1

%I #20 Jun 13 2022 08:02:15

%S 0,-1,0,9,0,1476225,0,32724184981958652351324462890625,0

%N Determinant of the adjacency matrix of the n-cube graph Q_n.

%D N. Biggs, Algebraic Graph Theory, Cambridge Univ. Press 1974, p. 145.

%H Alois P. Heinz, <a href="/A166734/b166734.txt">Table of n, a(n) for n = 0..12</a>

%F a(n) = Product_{j=0..n} (n-2j)^binomial(n,j).

%e a(3) = (3^1)*(1^3)*((-1)^3)*((-3)^1) = 3*1*(-1)*(-3) = 9.

%p a:= n-> mul((n-2*j)^binomial(n, j), j=0..n):

%p seq(a(n), n=0..9); # _Alois P. Heinz_, Jun 12 2022

%o (PARI) a(n) = prod(j=0, n, (n-2*j)^binomial(n,j)); \\ _Michel Marcus_, Feb 08 2020

%Y Cf. A229333.

%K sign,easy

%O 0,4

%A _Franz Vrabec_, Oct 20 2009