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A241881 Number of ascent sequences of length n with the maximal number of descents. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 17 17:25 EDT 2017. Contains 290648 sequences.