A306675 - OEIS

%I #10 Apr 02 2021 14:05:19

%S 0,1,15,455,25487,2293839,302786759,55107190151,13225725636255,

%T 4047072044694047,1537887376983737879,710503968166486900119,

%U 392198190427900768865711,254928823778135499762712175,192726190776270437820610404327,167671785975355280903931051764519

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

%H Alois P. Heinz, <a href="/A306675/b306675.txt">Table of n, a(n) for n = 0..224</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%F a(n) = A306506(2n,n).

%F a(n) = (2n)! - A306535(n).

%p b:= proc(n, k) b(n, k):= `if`(k=0, n!, b(n+1, k-1) -b(n, k-1)) end:

%p a:= n-> (2*n)! -b(0, 2*n):

%p seq(a(n), n=0..16);

%t b[n_, k_] := b[n, k] = If[k == 0, n!, b[n + 1, k - 1] - b[n, k - 1]];

%t a[n_] := (2n)! - b[0, 2n];

%t a /@ Range[0, 16] (* _Jean-François Alcover_, Apr 02 2021, after _Alois P. Heinz_ *)

%Y Cf. A306506, A306535.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Mar 04 2019