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

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Keywords

• nonn

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

Crossrefs

Column k=3 of A238123.

Programs

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 *)