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%I #21 Jan 19 2019 06:40:36
%S 0,0,1,0,2,5,14,35,132,399,1556,5346,21515,82940,351298,1470859,
%T 6559568,29273847,137203616,647330760,3177545635,15754135608,
%U 80674471962,418173444944,2226807020143,12017943310050,66375955944554,371721782181000,2124422025178277
%N Number of ballot sequences of length n having 2 largest parts.
%C Also number of standard Young tableaux with last row of length 2.
%H Alois P. Heinz, <a href="/A244099/b244099.txt">Table of n, a(n) for n = 0..85</a> (updated by Alois P. Heinz, Jan 19 2019)
%t 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 *)
%o (PARI) A244099(n)=A238123(n,2) \\ _M. F. Hasler_, Jun 03 2018
%Y Column k=2 of A238123.
%K nonn
%O 0,5
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014
%E a(0)=a(1)=0 prepended by _M. F. Hasler_, Jun 03 2018
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