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 A085807 Permanent of the symmetric n X n matrix A defined by A[i,j] = |i-j| for 1 <= i,j <= n. 10
 1, 0, 1, 4, 64, 1152, 34372, 1335008, 69599744, 4577345152, 374491314176, 37154032517376, 4402467119882240, 613680867638476800, 99443966100565999872, 18534733913629064343552, 3937496200758879526977536, 945776134421421651222708224, 255043190756805184245158084608 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Conjecture: For any odd prime p, we have a(p) == -1/2 (mod p). - Zhi-Wei Sun, Aug 30 2021 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..37 Zhi-Wei Sun, Arithmetic properties of some permanents, arXiv:2108.07723 [math.GM], 2021. MAPLE with(LinearAlgebra): a:= n-> `if`(n=0, 1, Permanent(Matrix(n, (i, j)-> abs(i-j)))): seq(a(n), n=0..18);  # Alois P. Heinz, Nov 14 2016 PROG (PARI) permRWNb(a)= n=matsize(a)[1]; if(n==1, return(a[1, 1])); sg=1; in=vectorv(n); x=in; x=a[, n]-sum(j=1, n, a[, j])/2; p=prod(i=1, n, x[i]); for(k=1, 2^(n-1)-1, sg=-sg; j=valuation(k, 2)+1; z=1-2*in[j]; in[j]+=z; x+=z*a[, j]; p+=prod(i=1, n, x[i], sg)); return(2*(2*(n%2)-1)*p) for(n=1, 22, a=matrix(n, n, i, j, abs(i-j)); print1(permRWNb(a)", ")) \\  Herman Jamke (hermanjamke(AT)fastmail.fm), May 14 2007 (PARI) {a(n) = matpermanent(matrix(n, n, i, j, abs(i-j)))} for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Aug 12 2021 (Python) from sympy import Matrix def A085807(n): return Matrix(n, n, [abs(j-k) for j in range(n) for k in range(n)]).per() # Chai Wah Wu, Sep 14 2021 CROSSREFS Cf. A085750, A204249, A278845, A278847. Sequence in context: A013709 A139292 A152923 * A014729 A322519 A259272 Adjacent sequences:  A085804 A085805 A085806 * A085808 A085809 A085810 KEYWORD nonn AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Jul 24 2003 EXTENSIONS More terms from Vladeta Jovovic, Jul 26 2003 a(0)=1 prepended by Alois P. Heinz, Nov 14 2016 STATUS approved

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Last modified July 2 12:24 EDT 2022. Contains 355004 sequences. (Running on oeis4.)