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

0,5

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)

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 *)

Prog

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

Crossrefs

Column k=2 of A238123.

Sequence in context: A131408 A137917 A360031 * A201371 A244061 A297120

Adjacent sequences: A244096 A244097 A244098 * A244100 A244101 A244102

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 20 2014

Extensions

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

Status

approved