A244102 Number of ballot sequences of length n having 5 largest parts.

1, 0, 0, 0, 0, 42, 132, 297, 572, 1001, 7644, 38584, 227460, 880668, 3560106, 13136733, 53948258, 260567615, 1322074776, 7132302760, 36927209090, 189472194730, 965322122310, 4935547435455, 26391699530094, 143808787394511, 824237501959916, 4756694235326336

Offset

5,6

Comments

Also number of standard Young tableaux with last row of length 5.

Links

Alois P. Heinz, Table of n, a(n) for n = 5..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, 5]; Table[a[n], {n, 5, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

Crossrefs

Column k=5 of A238123.

Sequence in context: A299362 A304613 A005557 * A045088 A303860 A002759

Adjacent sequences: A244099 A244100 A244101 * A244103 A244104 A244105

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved