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%I #8 Feb 10 2015 08:45:04
%S 1,0,0,0,0,42,132,297,572,1001,7644,38584,227460,880668,3560106,
%T 13136733,53948258,260567615,1322074776,7132302760,36927209090,
%U 189472194730,965322122310,4935547435455,26391699530094,143808787394511,824237501959916,4756694235326336
%N Number of ballot sequences of length n having 5 largest parts.
%C Also number of standard Young tableaux with last row of length 5.
%H Alois P. Heinz, <a href="/A244102/b244102.txt">Table of n, a(n) for n = 5..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, 5]; Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)
%Y Column k=5 of A238123.
%K nonn
%O 5,6
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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