A244104 Number of ballot sequences of length n having 7 largest parts.

1, 0, 0, 0, 0, 0, 0, 429, 1430, 3432, 7072, 13260, 23256, 38760, 1447686, 9241353, 61760336, 263673564, 1154175880, 4037346170, 14498731260, 58819097610, 288661103640, 1967198408955, 12613467934524, 82682367942144, 480369377259200, 2684682541268112

Offset

7,8

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 7..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, 7]; Table[a[n], {n, 7, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

Crossrefs

Column k=7 of A238123.

Sequence in context: A034278 A116870 A064061 * A115133 A090200 A033279

Adjacent sequences: A244101 A244102 A244103 * A244105 A244106 A244107

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved