A244104 - OEIS

%I #8 Feb 10 2015 08:45:17

%S 1,0,0,0,0,0,0,429,1430,3432,7072,13260,23256,38760,1447686,9241353,

%T 61760336,263673564,1154175880,4037346170,14498731260,58819097610,

%U 288661103640,1967198408955,12613467934524,82682367942144,480369377259200,2684682541268112

%N Number of ballot sequences of length n having 7 largest parts.

%C Also number of standard Young tableaux with last row of length 7.

%H Alois P. Heinz, <a href="/A244104/b244104.txt">Table of n, a(n) for n = 7..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, 7]; Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, Feb 10 2015, after A238123 *)

%Y Column k=7 of A238123.

%K nonn

%O 7,8

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014