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Number of permutations p of [2n+2] such that min_{j=1..2n+2} |p(j)-j| = n;
2

%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