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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A299164 A131408 A137917 * 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

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Last modified April 7 04:08 EDT 2020. Contains 333292 sequences. (Running on oeis4.)