0,4

Alois P. Heinz, Table of n, a(n) for n = 0..466

a(0) = 1: the empty permutation.

a(1) = 1: 1.

a(2) = 1: 12.

a(3) = 2: 123, 321.

a(4) = 8: 1234, 1432, 2413, 2431, 3214, 3412, 4213, 4231.

a(5) = 36: 12345, 12543, 13524, 13542, 14325, 14523, 15324, 15342, 24135, 24153, 24315, 24351, 24513, 24531, 31524, 31542, 32145, 32541, 34125, 34521, 35124, 35142, 42135, 42153, 42315, 42351, 42513, 42531, 51324, 51342, 52143, 52341, 53124, 53142, 54123, 54321.

b:= proc(n, i, j, p, t) option remember; `if`(n=0, 1,

`if`(i=0 or t=1 and p=1, 0, i*b(n-1, i-1, j, 1-p, p))+

`if`(j=0 or t=1 and p=0, 0, j*b(n-1, i, j-1, 1-p, 1-p)))

end:

a:= n-> b(n, floor(n/2), ceil(n/2), 1, 0):

seq(a(n), n=0..25);

b[n_, i_, j_, p_, t_] := b[n, i, j, p, t] =

If[n==0, 1, If[i==0 || t ==1 && p==1, 0, i*b[n-1, i-1, j, 1-p, p]] +

If[j==0 || t==1 && p==0, 0, j*b[n-1, i, j-1, 1-p, 1-p]]];

a[n_] := b[n, Floor[n/2], Ceiling[n/2], 1, 0];

Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Aug 30 2021, after Alois P. Heinz *)

Cf. A199660, A231601.

Sequence in context: A391129 A245102 A129148 * A081958 A369619 A316663

Adjacent sequences: A285669 A285670 A285671 * A285673 A285674 A285675

Alois P. Heinz, Apr 24 2017

approved