A306545 Number of permutations p of [2n+2] such that min_{j=1..2n+2} |p(j)-j| = n.

1, 8, 28, 111, 435, 1707, 6723, 26571, 105315, 418347, 1664643, 6632331, 26450595, 105566187, 421556163, 1684098891, 6730018275, 26900941227, 107546369283, 430013290251, 1719536600355, 6876596719467, 27501737832003, 109993004190411, 439930175348835

Offset: 0

Author

Alois P. Heinz, Feb 22 2019

Keywords

• nonn
• easy

Examples

			a(1) = 8: 2143, 2341, 2413, 3142, 3421, 4123, 4312, 4321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1660
• Wikipedia, Permutation
• Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

Crossrefs

Cf. A299789.

Formula

G.f.: (17*x^4-27*x^3+17*x^2-1)/(12*x^3-19*x^2+8*x-1).

a(n) = A299789(2n+2,n).