A229066 Number of 1 up, 2 down, 3 up, 4 down, ... permutations of [n].

1, 1, 1, 2, 3, 11, 26, 50, 315, 1168, 3309, 7910, 78134, 431354, 1748956, 5797168, 16619603, 239887424, 1875375485, 10496708022, 47013492080, 178807998112, 599025922320, 11965846097382, 126883998286089, 947079890934441, 5574231845278396, 27500583638094490

Offset: 0

Author

Alois P. Heinz, Oct 02 2013

Keywords

• nonn
• eigen

Examples

			a(2) = 1: 12.
a(3) = 2: 132, 231.
a(4) = 3: 1432, 2431, 3421.
a(5) = 11: 14325, 15324, 15423, 24315, 25314, 25413, 34215, 35214, 35412, 45213, 45312.
a(6) = 26: 143256, 153246, ..., 563124, 564123.
a(7) = 50: 1432567, 1532467, ..., 6741235, 6751234.
a(8) = 315: 14325687, 14325786, ..., 78613452, 78623451.
		

Links

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

Crossrefs

Cf. A227941, A229551, A229892.

Programs

Maple

b:= proc(u, o, t, k) option remember; `if`(u+o=0, 1, add(`if`(t=k,
       b(o-j, u+j-1, 1, k+1), b(u+j-1, o-j, t+1, k)), j=1..o))
    end:
a:= n-> b(0, n, 0, 1):
seq(a(n), n=0..35);

Mathematica

b[u_, o_, t_, k_] := b[u, o, t, k] = If[u + o == 0, 1, Sum[If[t == k, b[o - j, u + j - 1, 1, k + 1], b[u + j - 1, o - j, t + 1, k]], {j, 1, o}]];
a[n_] := b[0, n, 0, 1];
a /@ Range[0, 35] (* Jean-François Alcover, Mar 22 2021, after Alois P. Heinz *)