A244106 Number of ballot sequences of length n having 9 largest parts.

1, 0, 0, 0, 0, 0, 0, 0, 0, 4862, 16796, 41990, 90440, 177650, 326876, 572033, 961400, 1562275, 416782080, 2904006105, 20591110410, 93272863125, 429784750200, 1588873361400, 5988317533044, 19637330636352, 65753496366140, 376581209597560, 2635731247693060

Offset

9,10

Comments

Also number of standard Young tableaux with last row of length 9.

Links

Alois P. Heinz, Table of n, a(n) for n = 9..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, 9]; Table[a[n], {n, 9, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

Crossrefs

Column k=9 of A238123.

Sequence in context: A031826 A243835 A124088 * A264182 A258496 A258397

Adjacent sequences: A244103 A244104 A244105 * A244107 A244108 A244109

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved