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%I #12 Feb 24 2019 15:34:32
%S 1,8,28,111,435,1707,6723,26571,105315,418347,1664643,6632331,
%T 26450595,105566187,421556163,1684098891,6730018275,26900941227,
%U 107546369283,430013290251,1719536600355,6876596719467,27501737832003,109993004190411,439930175348835
%N Number of permutations p of [2n+2] such that min_{j=1..2n+2} |p(j)-j| = n;
%H Alois P. Heinz, <a href="/A306545/b306545.txt">Table of n, a(n) for n = 0..1660</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).
%F G.f.: (17*x^4-27*x^3+17*x^2-1)/(12*x^3-19*x^2+8*x-1).
%F a(n) = A299789(2n+2,n).
%e a(1) = 8: 2143, 2341, 2413, 3142, 3421, 4123, 4312, 4321.
%Y Cf. A299789.
%K nonn,easy
%O 0,2
%A _Alois P. Heinz_, Feb 22 2019