%I #12 Jan 28 2019 10:49:49
%S 0,10,47,157,503,1669,5472,17531,55135,172134,535510,1660795,5133470,
%T 15826173,48706210,149721544,459820058,1411142937,4328181110,
%U 13269541967,40669595890,124617708274,381776661185,1169438884559,3581781480980,10969462410857,33592685042253
%N Number of permutations p of [n] such that max_{j=1..n} |p(j)-j| = 3.
%H Alois P. Heinz, <a href="/A323799/b323799.txt">Table of n, a(n) for n = 3..1000</a>
%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-2,6,-17,-16,-30,6,32,48,12,-16,-16,-9,2,-2,-2,2,1).
%F G.f.: x^4 *(x^11+x^10-3*x^9+x^8+4*x^7-4*x^6-4*x^5-5*x^4+11*x^3+11*x^2-7*x-10) / ((x-1) *(x^5 -2*x^3 -2*x+1) *(x^13 +3*x^12 +3*x^11 +5*x^10 +9*x^9 +7*x^8 -3*x^7 -19*x^6 -21*x^5 -13*x^4 -3*x^3 -3*x^2-x+1)).
%F a(n) = A002526(n) - A002524(n).
%e a(4) = 10: 2341, 2431, 3241, 3421, 4123, 4132, 4213, 4231, 4312, 4321.
%Y Column k=3 of A130152.
%Y Cf. A002524, A002526.
%K nonn,easy
%O 3,2
%A _Alois P. Heinz_, Jan 28 2019
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