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A306675 Number of permutations p of [2n] having at least one index i with |p(i)-i| = n.

%I A306675 #10 Apr 02 2021 14:05:19
%S A306675 0,1,15,455,25487,2293839,302786759,55107190151,13225725636255,
%T A306675 4047072044694047,1537887376983737879,710503968166486900119,
%U A306675 392198190427900768865711,254928823778135499762712175,192726190776270437820610404327,167671785975355280903931051764519
%N A306675 Number of permutations p of [2n] having at least one index i with |p(i)-i| = n.
%H A306675 Alois P. Heinz, <a href="/A306675/b306675.txt">Table of n, a(n) for n = 0..224</a>
%H A306675 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A306675 a(n) = A306506(2n,n).
%F A306675 a(n) = (2n)! - A306535(n).
%p A306675 b:= proc(n, k) b(n, k):= `if`(k=0, n!, b(n+1, k-1) -b(n, k-1)) end:
%p A306675 a:= n-> (2*n)! -b(0, 2*n):
%p A306675 seq(a(n), n=0..16);
%t A306675 b[n_, k_] := b[n, k] = If[k == 0, n!, b[n + 1, k - 1] - b[n, k - 1]];
%t A306675 a[n_] := (2n)! - b[0, 2n];
%t A306675 a /@ Range[0, 16] (* _Jean-François Alcover_, Apr 02 2021, after _Alois P. Heinz_ *)
%Y A306675 Cf. A306506, A306535.
%K A306675 nonn
%O A306675 0,3
%A A306675 _Alois P. Heinz_, Mar 04 2019