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

10,11

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

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 *)

Crossrefs

Column k=10 of A238123.

Sequence in context: A053074 A115923 A243836 * A264183 A258497 A258398

Adjacent sequences: A244104 A244105 A244106 * A244108 A244109 A244110

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved