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A244107 Number of ballot sequences of length n having 10 largest parts. 2

%I

%S 1,0,0,0,0,0,0,0,0,0,16796,58786,149226,326876,653752,1225785,2187185,

%T 3749460,6216210,10015005,7661738955,54722507580,395948080320,

%U 1833749903700,8617567868184,32552623293036,125052931581776,418634577697116,1427554615084576

%N Number of ballot sequences of length n having 10 largest parts.

%C Also number of standard Young tableaux with last row of length 10.

%H Alois P. Heinz, <a href="/A244107/b244107.txt">Table of n, a(n) for n = 10..100</a>

%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, 10]; Table[a[n], {n, 10, 30}] (* _Jean-Fran├žois Alcover_, Feb 10 2015, after A238123 *)

%Y Column k=10 of A238123.

%K nonn

%O 10,11

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 20 2014

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Last modified June 21 11:18 EDT 2021. Contains 345362 sequences. (Running on oeis4.)