A241871 Number of ascent sequences of length 2n with exactly n descents.

1, 0, 0, 1, 26, 937, 45747, 2945144, 242899690, 25034354941, 3157647587689, 478931493603308, 86057396214591300, 18086772915953351382, 4397414569504319733812, 1224945090342466220614714, 387654163770235904289085798, 138333762956844287480268151988

Offset

0,5

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..70

Formula

a(n) = A238858(2n,n).

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1, expand(add(
      `if`(j<i, x, 1) *b(n-1, j, t+`if`(j>i, 1, 0)), j=0..t+1)))
    end:
a:= n-> coeff(b(2*n, -1$2), x, n):
seq(a(n), n=0..20);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[If[j<i, x, 1]*b[n-1, j, t + If[j>i, 1, 0]], {j, 0, t+1}]]]; a[n_] := Coefficient[b[2*n, -1, -1], x, n]; Table[ a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 13 2015, after Maple *)

Crossrefs

Cf. A238858.

Sequence in context: A333117 A263945 A335609 * A160261 A357376 A241874

Adjacent sequences: A241868 A241869 A241870 * A241872 A241873 A241874

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 01 2014

Status

approved