A195422 - OEIS

%I #12 Jun 07 2021 13:39:40

%S -3,2,2,-8,16,-16,80,384,4160,43008,494336,6136832,82118656,

%T 1178294272,18053433344,294241402880,5083946115072,92835116318720,

%U 1786595439869952,36144509314138112,766933328068345856

%N Permanents of certain n X 2 cyclic (1,-1) matrices.

%H A. R. Krauter, <a href="http://www.mat.univie.ac.at/~slc/opapers/s11kraeu.html">Uber die Permanente gewisser Matrizen und damit zusammenhangender...</a>, Sem. Loth. Combinat. B11B (1984) 82-94, eq. (3.12)

%F a(n) = Sum_{k=0..n} (-2)^k*2*n*binomial(2*n-k,k)*(n-k)!/(2*n-k).

%F a(n) ~ exp(-4) * n!. - _Vaclav Kotesovec_, Dec 17 2015

%F Conjecture: (-n+2)*a(n) +(n^2-4*n+6)*a(n-1) +2*(n^2-2*n+3)*a(n-2) +8*(n-1)*a(n-3) = 0. - _R. J. Mathar_, Jul 20 2016

%F Conjecture: a(n) -n*a(n-1) -8*a(n-2) +4*(n-4)*a(n-3) +16*a(n-4) = 0. - _R. J. Mathar_, Jul 20 2016

%p A195422 := proc(n)

%p     local k;

%p     add((-2)^k*2*n*binomial(2*n-k,k)*(n-k)!/(2*n-k),k=0..n) ;

%p end proc: # _R. J. Mathar_, Jul 20 2016

%t Table[Sum[(-2)^k*2*n*Binomial[2*n - k, k]*(n - k)!/(2*n - k), {k, 0, n}], {n, 1, 20}] (* _Vaclav Kotesovec_, Dec 17 2015 *)

%K sign,easy

%O 1,1

%A _R. J. Mathar_, Sep 18 2011