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%I #8 Feb 10 2015 08:45:21
%S 1,0,0,0,0,0,0,0,1430,4862,11934,25194,48450,87210,149226,245157,
%T 23761001,159952925,1105745355,4877504775,21957739245,79151445945,
%U 291770177400,934243294725,4553273607924,25467623215188,210714037216628,1472412825136220
%N Number of ballot sequences of length n having 8 largest parts.
%C Also number of standard Young tableaux with last row of length 8.
%H Alois P. Heinz, <a href="/A244105/b244105.txt">Table of n, a(n) for n = 8..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, 8]; Table[a[n], {n, 8, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)
%Y Column k=8 of A238123.
%K nonn
%O 8,9
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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