A199660 Number of parity alternating permutations of [n] avoiding descents from odd to even numbers.

1, 1, 2, 1, 5, 2, 20, 6, 114, 24, 864, 120, 8280, 720, 96480, 5040, 1325520, 40320, 20966400, 362880, 374855040, 3628800, 7468070400, 39916800, 163938297600, 479001600, 3929729126400, 6227020800, 102104460057600, 87178291200, 2857878742118400, 1307674368000

Offset: 0

Author

Alois P. Heinz, Nov 08 2011

Keywords

• nonn
• easy

Examples

			a(4) = 5: (1,2,3,4), (2,1,4,3), (2,3,4,1), (3,4,1,2), (4,1,2,3).
a(5) = 2: (1,2,3,4,5), (3,4,1,2,5).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Crossrefs

Bisection gives: A052850 (even part, n>0), A000142 (odd part).

Column k=0 of A232187.

Cf. A285672.

Programs

Maple

a:= n-> `if`(n=0, 1, `if`(irem(n, 2, 'r')=0, (2^r+r-1)*(r-1)!, r!)):
seq(a(n), n=0..35);

Mathematica

a[n_] := If[n == 0, 1, With[{r = Quotient[n, 2]},
       If[Mod[n, 2] == 0, (2^r+r-1)(r-1)!, r!]]];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Oct 30 2021, after Alois P. Heinz *)

Formula

a(0) = 1, a(2*n) = (2^n+n-1)*(n-1)! for n>0, a(2*n+1) = n!.