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

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Keywords

• nonn

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

Crossrefs

Column k=4 of A238123.

Programs

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 *)