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%I #8 Feb 10 2015 08:45:26
%S 1,0,0,0,0,0,0,0,0,4862,16796,41990,90440,177650,326876,572033,961400,
%T 1562275,416782080,2904006105,20591110410,93272863125,429784750200,
%U 1588873361400,5988317533044,19637330636352,65753496366140,376581209597560,2635731247693060
%N Number of ballot sequences of length n having 9 largest parts.
%C Also number of standard Young tableaux with last row of length 9.
%H Alois P. Heinz, <a href="/A244106/b244106.txt">Table of n, a(n) for n = 9..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, 9]; Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)
%Y Column k=9 of A238123.
%K nonn
%O 9,10
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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