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%I #12 Oct 21 2023 11:34:34
%S 0,0,2,6,24,80,312,1152,4616,18384,77280,328352,1451712,6527616,
%T 30299504,143322000,696359232,3448656512,17483842176,90301959744,
%U 476270369600,2557007766912,13991998520832,77867819879936,441003737739264,2537848321044480,14843836828748672
%N Number of permutations p of [n] such that max(|p(p(i)) - i|)=1.
%F a(n) = Sum_{k=1..floor(n/4)} (n-2*k)! * A000085(n-4*k) / (k! * (n-4*k)!).
%Y Column k=1 of A364817.
%Y Cf. A000085.
%K nonn
%O 2,3
%A _Seiichi Manyama_, Oct 21 2023