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%I #8 Feb 10 2015 08:44:59
%S 1,0,0,0,14,42,90,165,737,3003,15652,55965,236924,851224,3872838,
%T 16766607,83026979,390791373,1941965432,9380708953,47629991554,
%U 241035098010,1284641489560,6852122431245,38078198632749,211138699725567,1208307893511470,6916339675763595
%N Number of ballot sequences of length n having 4 largest parts.
%C Also number of standard Young tableaux with last row of length 4.
%H Alois P. Heinz, <a href="/A244101/b244101.txt">Table of n, a(n) for n = 4..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, 4]; Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)
%Y Column k=4 of A238123.
%K nonn
%O 4,5
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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