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A244100
Number of ballot sequences of length n having 3 largest parts.
2
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
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
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jun 20 2014
STATUS
approved