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%I #14 Feb 06 2017 18:16:06
%S 26,56,132,327,863,2333,6620,19130,57515,175771,555673,1784015,
%T 5899056,19795308,68163789,238040835,850372635,3079156803,11376375381,
%U 42585665859,162324759308,626699226366,2459686799702,9775044096970,39436677372291,161037770577853
%N Number of standard Young tableaux with n cells and 6 as last value in the first row.
%C Also the number of ballot sequences of length n where 6 is the position of the last occurrence of the minimal value.
%H Joerg Arndt and Alois P. Heinz, <a href="/A245004/b245004.txt">Table of n, a(n) for n = 6..80</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%t b[n_, l_List] := b[n, l] = If[n == 0, 1, Sum[If[i == 1 || l[[i - 1]] > l[[i]], b[n - 1, ReplacePart[l, i -> l[[i]] + 1]], 0], {i, 1, Length[l]}] + Function[{p}, p + (x^(1 + Total[l]) - 1)*Coefficient[p, x, 0]][b[n - 1, Append[l, 1]]]]; a[n_] := Coefficient[b[n, {}], x, 6]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 6, 40}] (* _Jean-François Alcover_, Feb 06 2015, after Maple code in A238794 *)
%Y Column k=6 of A238794.
%K nonn
%O 6,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 09 2014
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