Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Feb 06 2017 18:17:57
%S 764,2031,5741,17088,52540,168172,551142,1866639,6448956,22908742,
%T 82853921,306971909,1156564466,4451496217,17407985332,69394132575,
%U 280851149296,1156692921549,4833132867603,20521962586186,88343703440840,386014928037316,1708872377386105
%N Number of standard Young tableaux with n cells and 9 as last value in the first row.
%C Also the number of ballot sequences of length n where 9 is the position of the last occurrence of the minimal value.
%H Joerg Arndt and Alois P. Heinz, <a href="/A245007/b245007.txt">Table of n, a(n) for n = 9..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, 9]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 9, 40}] (* _Jean-François Alcover_, Feb 06 2015, after Maple code in A238794 *)
%Y Column k=9 of A238794.
%K nonn
%O 9,1
%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 09 2014