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