A231601 - OEIS

%I #19 Dec 01 2019 12:17:00

%S 1,1,1,4,8,54,162,1536,6144,75000,375000,5598720,33592320,592950960,

%T 4150656720,84557168640,676457349120,15620794116480,140587147048320,

%U 3628800000000000,36288000000000000,1035338990313196800,11388728893445164800,355902198372945100800

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

%H Alois P. Heinz, <a href="/A231601/b231601.txt">Table of n, a(n) for n = 0..250</a>

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

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

%e a(0) = 1: ().

%e a(1) = 1: 1.

%e a(2) = 1: 21.

%e a(3) = 4: 132, 213, 231, 321.

%e a(4) = 8: 1324, 2413, 2431, 3241, 4132, 4213, 4231, 4321.

%e a(5) = 54: 13245, 13254, 13524, ..., 54213, 54231, 54321.

%e a(6) = 162: 132465, 132546, 132645, ..., 654213, 654231, 654321.

%p a:= n-> ceil(n/2)!*ceil(n/2)^floor(n/2):

%p seq(a(n), n=0..30);

%Y Column k=0 of A231777.

%Y Bisection gives: A061711 (even part).

%Y Cf. A081123, A110138, A199660, A285672.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Nov 11 2013