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

0,4

Links

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

Formula

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

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

Example

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.

Maple

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

Crossrefs

Column k=0 of A231777.

Bisection gives: A061711 (even part).

Cf. A081123, A110138, A199660, A285672.

Sequence in context: A128893 A214603 A192508 * A347511 A123106 A123288

Adjacent sequences: A231598 A231599 A231600 * A231602 A231603 A231604

Keyword

nonn

Author

Alois P. Heinz, Nov 11 2013

Status

approved