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%I #8 Feb 10 2015 08:45:12
%S 1,0,0,0,0,0,132,429,1001,2002,3640,6188,97512,569772,3625998,
%T 14847987,62772941,211719508,877100400,3621910050,21265454080,
%U 120016339560,727205489010,3972645105975,21545198606739,109895587819830,577299928495856,3037242685942432
%N Number of ballot sequences of length n having 6 largest parts.
%C Also number of standard Young tableaux with last row of length 6.
%H Alois P. Heinz, <a href="/A244103/b244103.txt">Table of n, a(n) for n = 6..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, 6]; Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)
%Y Column k=6 of A238123.
%K nonn
%O 6,7
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
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