A244107 Number of ballot sequences of length n having 10 largest parts.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16796, 58786, 149226, 326876, 653752, 1225785, 2187185, 3749460, 6216210, 10015005, 7661738955, 54722507580, 395948080320, 1833749903700, 8617567868184, 32552623293036, 125052931581776, 418634577697116, 1427554615084576

Offset: 10

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Keywords

• nonn

Comments

Also number of standard Young tableaux with last row of length 10.

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..100

Crossrefs

Column k=10 of A238123.

Programs

Mathematica

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, 10]; Table[a[n], {n, 10, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)