A244101 Number of ballot sequences of length n having 4 largest parts.

1, 0, 0, 0, 14, 42, 90, 165, 737, 3003, 15652, 55965, 236924, 851224, 3872838, 16766607, 83026979, 390791373, 1941965432, 9380708953, 47629991554, 241035098010, 1284641489560, 6852122431245, 38078198632749, 211138699725567, 1208307893511470, 6916339675763595

Offset

4,5

Comments

Also number of standard Young tableaux with last row of length 4.

Links

Alois P. Heinz, Table of n, a(n) for n = 4..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, 4]; Table[a[n], {n, 4, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

Crossrefs

Column k=4 of A238123.

Sequence in context: A356452 A163756 A005587 * A212514 A292051 A242897

Adjacent sequences: A244098 A244099 A244100 * A244102 A244103 A244104

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Status

approved