A244100 Number of ballot sequences of length n having 3 largest parts.

1, 0, 0, 5, 14, 28, 90, 285, 1232, 4378, 17082, 65338, 269775, 1148080, 5111730, 23047359, 107594036, 507358368, 2479868846, 12286215326, 62819732813, 325860325750, 1733254403460, 9356359893725, 51583509113814, 288761957868348, 1647416875806320

Offset

3,4

Comments

Also number of standard Young tableaux with last row of length 3.

Links

Alois P. Heinz, Table of n, a(n) for n = 3..100

Mathematica

b[n_, l_List] := b[n, l] = If[n < 1, x^l[[-1]], b[n - 1, Append[l, 1]] + Sum[If[i == 1 || l[[i - 1]] > l[[i]], b[n - 1, ReplacePart[l, i -> l[[i]] + 1]], 0], {i, 1, Length[l]}]]; a[n_] := Coefficient[b[n - 1, {1}], x, 3]; Table[a[n], {n, 3, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

Crossrefs

Column k=3 of A238123.

Sequence in context: A005586 A197058 A212678 * A031333 A303706 A161437

Adjacent sequences: A244097 A244098 A244099 * A244101 A244102 A244103

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved