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A364817 Triangle read by rows: T(n,k) = number of permutations p of [n] such that max(|p(p(i)) - i|)=k (n>=1, 0<=k<=n-1).

%I A364817 #20 Oct 22 2023 06:44:26
%S A364817 1,2,0,4,0,2,10,2,6,6,26,6,22,36,30,76,24,92,144,216,168,232,80,334,
%T A364817 640,1150,1524,1080,764,312,1328,2984,5516,9712,11784,7920,2620,1152,
%U A364817 5234,13296,27668,55750,90240,101400,65520,9496,4616,21780,62124,144564,306272,601756,909312,964080,604800
%N A364817 Triangle read by rows: T(n,k) = number of permutations p of [n] such that max(|p(p(i)) - i|)=k (n>=1, 0<=k<=n-1).
%F A364817 T(n,n-1) = (2*n-5)*(n-2)! for n>3.
%e A364817 Triangle starts:
%e A364817      1;
%e A364817      2,    0;
%e A364817      4,    0,    2;
%e A364817     10,    2,    6,     6;
%e A364817     26,    6,   22,    36,    30;
%e A364817     76,   24,   92,   144,   216,   168;
%e A364817    232,   80,  334,   640,  1150,  1524,  1080;
%e A364817    764,  312, 1328,  2984,  5516,  9712, 11784,   7920;
%e A364817   2620, 1152, 5234, 13296, 27668, 55750, 90240, 101400, 65520;
%Y A364817 Columns k=0..1 give: A000085, A364819.
%Y A364817 Row sums give A000142.
%Y A364817 Cf. A130152, A175925.
%K A364817 nonn,tabl
%O A364817 1,2
%A A364817 _Seiichi Manyama_, Oct 21 2023