A244099 Number of ballot sequences of length n having 2 largest parts.

0, 0, 1, 0, 2, 5, 14, 35, 132, 399, 1556, 5346, 21515, 82940, 351298, 1470859, 6559568, 29273847, 137203616, 647330760, 3177545635, 15754135608, 80674471962, 418173444944, 2226807020143, 12017943310050, 66375955944554, 371721782181000, 2124422025178277

Offset: 0

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Keywords

• nonn

Comments

Also number of standard Young tableaux with last row of length 2.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..85 (updated by Alois P. Heinz, Jan 19 2019)

Crossrefs

Column k=2 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, 2]; Table[a[n], {n, 2, 30}] (* Jean-François Alcover, Feb 10 2015, after A238123 *)

PARI

A244099(n)=A238123(n,2) \\ M. F. Hasler, Jun 03 2018

Extensions

a(0)=a(1)=0 prepended by M. F. Hasler, Jun 03 2018