A227941 - OEIS

%I #22 Sep 01 2022 04:58:55

%S 1,1,1,2,3,4,19,55,125,245,434,4060,21186,81212,254813,692678,1688555,

%T 3776432,60101767,511650887,3089821383,14824989723,60057570858,

%U 213302293918,681247718668,1992449334436,5409214694961,132273848506202,1692162553490943

%N Number of 1 up, 3 down, 5 up, 7 down, ... permutations of [n].

%H Alois P. Heinz, <a href="/A227941/b227941.txt">Table of n, a(n) for n = 0..300</a>

%e a(2) = 1: 12.

%e a(3) = 2: 132, 231.

%e a(4) = 3: 1432, 2431, 3421.

%e a(5) = 4: 15432, 25431, 35421, 45321.

%e a(6) = 19: 154326, 164325, 165324, 165423, 254316, 264315, 265314, 265413, 354216, 364215, 365214, 365412, 453216, 463215, 465213, 465312, 563214, 564213, 564312.

%e a(7) = 55: 1543267, 1643257, ..., 6753124, 6754123.

%e a(8) = 125: 15432678, 16432578, ..., 78641235, 78651234.

%p b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1, add(`if`(t=2*k-1,

%p        b(o-j, u+j-1, 1, k+1), b(u+j-1, o-j, t+1, k)), j=1..o))

%p     end:

%p a:= n-> b(0, n, 0, 1):

%p seq(a(n), n=0..35);

%t b[u_, o_, t_, k_] := b[u, o, t, k] = If[u+o == 0, 1, Sum[If[t == 2*k-1, b[o-j, u+j-1, 1, k+1], b[u+j-1, o-j, t+1, k]], {j, 1, o}]];

%t a[n_] := b[0, n, 0, 1];

%t Table[a[n], {n, 0, 35}] (* _Jean-François Alcover_, Sep 01 2022, after _Alois P. Heinz_ *)

%Y Cf. A005408, A229066, A229551, A229892.

%K nonn,eigen

%O 0,4

%A _Alois P. Heinz_, Oct 03 2013