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

0,3

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

Formula

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

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-> (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[j<i, x, 1] *b[n-1, j, t + If[j>i, 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 *)

Crossrefs

Sequence in context: A011274 A122843 A167196 * A107865 A089225 A185110

Adjacent sequences: A241878 A241879 A241880 * A241882 A241883 A241884

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, May 01 2014

Status

approved