A231601 Number of permutations of [n] avoiding ascents from odd to even numbers.

1, 1, 1, 4, 8, 54, 162, 1536, 6144, 75000, 375000, 5598720, 33592320, 592950960, 4150656720, 84557168640, 676457349120, 15620794116480, 140587147048320, 3628800000000000, 36288000000000000, 1035338990313196800, 11388728893445164800, 355902198372945100800

Offset: 0

Author

Alois P. Heinz, Nov 11 2013

Keywords

• nonn

Examples

			a(0) = 1: ().
a(1) = 1: 1.
a(2) = 1: 21.
a(3) = 4: 132, 213, 231, 321.
a(4) = 8: 1324, 2413, 2431, 3241, 4132, 4213, 4231, 4321.
a(5) = 54: 13245, 13254, 13524, ..., 54213, 54231, 54321.
a(6) = 162: 132465, 132546, 132645, ..., 654213, 654231, 654321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..250

Crossrefs

Column k=0 of A231777.

Bisection gives: A061711 (even part).

Cf. A081123, A110138, A199660, A285672.

Programs

Maple

a:= n-> ceil(n/2)!*ceil(n/2)^floor(n/2):
seq(a(n), n=0..30);

Formula

a(n) = ceiling(n/2)! * ceiling(n/2)^floor(n/2).

a(n) = A081123(n+1) * A110138(n).