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%I #8 Feb 10 2015 08:44:55
%S 1,0,0,5,14,28,90,285,1232,4378,17082,65338,269775,1148080,5111730,
%T 23047359,107594036,507358368,2479868846,12286215326,62819732813,
%U 325860325750,1733254403460,9356359893725,51583509113814,288761957868348,1647416875806320
%N Number of ballot sequences of length n having 3 largest parts.
%C Also number of standard Young tableaux with last row of length 3.
%H Alois P. Heinz, <a href="/A244100/b244100.txt">Table of n, a(n) for n = 3..100</a>
%t 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 *)
%Y Column k=3 of A238123.
%K nonn
%O 3,4
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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