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A134293 Number of ways to pair up {2..2n+1} so the sum of each pair is prime.

%I A134293 #15 Aug 20 2021 03:31:25
%S A134293 1,1,2,6,20,60,190,764,2337,9812,49538,330058,2133438,11192143,
%T A134293 73469550,462692414,3692965270,32635321384,290171883863,2572828730372,
%U A134293 22299380503953,195129375058656,1544534855847233,13144353749969945,128883813733449772,1365629506139662111
%N A134293 Number of ways to pair up {2..2n+1} so the sum of each pair is prime.
%C A134293 This sequence complements A000341, which is also related to A073364.
%H A134293 Vaclav Kotesovec, <a href="/A134293/b134293.txt">Table of n, a(n) for n = 1..35</a>
%F A134293 a(n) = permanent(m), where the n X n matrix m is defined by m(i,j) = 1 or 0, depending on whether 2i+2j+1 is prime or composite, respectively.
%e A134293 a(3)=2 because for the set {2..7} there are two ways: {{2,3},{4,7},{5,6}} and {{2,5},{3,4},{6,7}}.
%t A134293 a[n_] := Permanent[Array[Boole[PrimeQ[2 #1 + 2 #2 + 1]]&, {n, n}]];
%t A134293 Array[a, 15] (* _Jean-François Alcover_, Nov 03 2018 *)
%o A134293 (PARI) a(n)={matpermanent(matrix(n,n,i,j,isprime(2*i + 2*j + 1)))} \\ _Andrew Howroyd_, Nov 03 2018
%K A134293 nonn
%O A134293 1,3
%A A134293 _T. D. Noe_, Oct 17 2007
%E A134293 a(21)-a(26) from _Andrew Howroyd_, Nov 03 2018