A266947 Number of permutations p of [2n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value of n.

1, 1, 11, 130, 4734, 127538, 11174035, 554432537, 92953037066, 7392808621010, 2037044419366071, 237281497432517293, 97619260603080874874, 15664643539583989506694, 9013597510492035989870645, 1906222253095637349478735538, 1463288823474568248157186058298

Offset

0,3

Links

Alois P. Heinz and Vaclav Kotesovec, Table of n, a(n) for n = 0..168 (terms 0..100 from Alois P. Heinz)

Formula

a(n) = A258829(2n,n).

Example

a(2) = 11: 1324, 1423, 1432, 2134, 2314, 2413, 2431, 3124, 3412, 3421, 4123.

Maple

b:= proc(u, o, c, k) option remember;
      `if`(c<0 or c>k, 0, `if`(u+o=0, 1,
       add(b(u-j, o-1+j, c+1, k), j=1..u)+
       add(b(u+j-1, o-j, c-1, k), j=1..o)))
    end:
a:= n-> b(2*n, 0$2, n)-b(2*n, 0$2, n-1):
seq(a(n), n=0..20);

Mathematica

b[u_, o_, c_, k_] := b[u, o, c, k] = If[c < 0 || c > k, 0, If[u + o == 0, 1, Sum[b[u - j, o - 1 + j, c + 1, k], {j, 1, u}] + Sum[b[u + j - 1, o - j, c - 1, k], {j, 1, o}]]];
a[n_] := b[2n, 0, 0, n] - b[2n, 0, 0, n - 1];
a /@ Range[0, 20] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)

Crossrefs

Cf. A258829.

Sequence in context: A183837 A015603 A184280 * A157718 A256957 A046210

Adjacent sequences: A266944 A266945 A266946 * A266948 A266949 A266950

Keyword

nonn

Author

Alois P. Heinz, Jan 06 2016

Status

approved