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

%I A231601 #19 Dec 01 2019 12:17:00
%S A231601 1,1,1,4,8,54,162,1536,6144,75000,375000,5598720,33592320,592950960,
%T A231601 4150656720,84557168640,676457349120,15620794116480,140587147048320,
%U A231601 3628800000000000,36288000000000000,1035338990313196800,11388728893445164800,355902198372945100800
%N A231601 Number of permutations of [n] avoiding ascents from odd to even numbers.
%H A231601 Alois P. Heinz, <a href="/A231601/b231601.txt">Table of n, a(n) for n = 0..250</a>
%F A231601 a(n) = ceiling(n/2)! * ceiling(n/2)^floor(n/2).
%F A231601 a(n) = A081123(n+1) * A110138(n).
%e A231601 a(0) = 1: ().
%e A231601 a(1) = 1: 1.
%e A231601 a(2) = 1: 21.
%e A231601 a(3) = 4: 132, 213, 231, 321.
%e A231601 a(4) = 8: 1324, 2413, 2431, 3241, 4132, 4213, 4231, 4321.
%e A231601 a(5) = 54: 13245, 13254, 13524, ..., 54213, 54231, 54321.
%e A231601 a(6) = 162: 132465, 132546, 132645, ..., 654213, 654231, 654321.
%p A231601 a:= n-> ceil(n/2)!*ceil(n/2)^floor(n/2):
%p A231601 seq(a(n), n=0..30);
%Y A231601 Column k=0 of A231777.
%Y A231601 Bisection gives: A061711 (even part).
%Y A231601 Cf. A081123, A110138, A199660, A285672.
%K A231601 nonn
%O A231601 0,4
%A A231601 _Alois P. Heinz_, Nov 11 2013