A241881 Number of ascent sequences of length n with the maximal number of descents.

1, 1, 2, 1, 7, 4, 1, 48, 26, 8, 1, 594, 262, 76, 13, 1, 10030, 3571, 933, 169, 19, 1, 205271, 61206, 14351, 2550, 323, 26, 1, 4910802, 1263620, 267378, 45321, 5918, 559, 34, 1, 134636523, 30534920, 5873492, 939681, 121689, 12257, 901, 43, 1, 4166817191

Offset: 0

Author

Joerg Arndt and Alois P. Heinz, May 01 2014

Keywords

• nonn

Comments

a(n*(n+1)/2) = a(A000217(n)) = 1.

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 0..140

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, 1, expand(add(
      `if`(ji, 1, 0)), j=0..t+1)))
    end:
a:= n-> (p-> coeff(p, x, degree(p)))(b(n, -1$2)):
seq(a(n), n=0..40);

Mathematica

b[n_, i_, t_] := b[n, i, t] = If[n == 0, 1, Expand[Sum[If[ji, 1, 0]], {j, 0, t+1}]]]; a[n_] := Function[{p}, Coefficient[p, x, Exponent[ p, x ]]][b[n, -1, -1]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Feb 13 2015, after Maple *)

Formula

a(n) = A238858(n,Re(n-floor((sqrt(8*n-7)+1)/2))).