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

0,3

Links

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

Formula

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

Example

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).

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 *)

Crossrefs

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

Column k=0 of A232187.

Cf. A285672.

Sequence in context: A194092 A140165 A185131 * A367671 A141483 A230038

Adjacent sequences: A199657 A199658 A199659 * A199661 A199662 A199663

Keyword

nonn,easy

Author

Alois P. Heinz, Nov 08 2011

Status

approved