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%I #11 Feb 06 2017 18:18:34
%S 2620,7408,22088,68576,221715,736624,2528896,8873588,32006883,
%T 117678413,443117232,1698040262,6645905493,26440507207,107212883073,
%U 441495784378,1849869784105,7864963647493,33977806366991,148834877695923,661707905560864,2980829993379396
%N Number of standard Young tableaux with n cells and 10 as last value in the first row.
%C Also the number of ballot sequences of length n where 10 is the position of the last occurrence of the minimal value.
%H Joerg Arndt and Alois P. Heinz, <a href="/A245008/b245008.txt">Table of n, a(n) for n = 10..50</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, 10]; Table[Print["a(", n, ") = ", an = a[n]]; an, {n, 10, 40}] (* _Jean-François Alcover_, Feb 06 2015, after Maple code in A238794 *)
%Y Column k=10 of A238794.
%K nonn
%O 10,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 09 2014
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