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A245006 Number of standard Young tableaux with n cells and 8 as last value in the first row. 2

%I #11 Feb 06 2017 18:17:21

%S 232,582,1563,4384,12939,39198,123629,398003,1324715,4489759,15653882,

%T 55503161,201686249,744669554,2809714695,10764956657,42053547589,

%U 166724084605,672761983296,2753474296366,11453358056417,48292313841411,206690703254636,896160453214130

%N Number of standard Young tableaux with n cells and 8 as last value in the first row.

%C Also the number of ballot sequences of length n where 8 is the position of the last occurrence of the minimal value.

%H Joerg Arndt and Alois P. Heinz, <a href="/A245006/b245006.txt">Table of n, a(n) for n = 8..50</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%t b[n_, l_List] := b[n, l] = If[n == 0, 1, Sum[If[i == 1 || l[[i - 1]] > l[[i]], b[n - 1, ReplacePart[l, i -> l[[i]] + 1]], 0], {i, 1, Length[l]}] + Function[{p}, p + (x^(1 + Total[l]) - 1)*Coefficient[p, x, 0]][b[n - 1, Append[l, 1]]]]; a[n_] := Coefficient[b[n, {}], x, 8]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 8, 40}] (* _Jean-François Alcover_, Feb 06 2015, after Maple code in A238794 *)

%Y Column k=8 of A238794.

%K nonn

%O 8,1

%A _Joerg Arndt_ and _Alois P. Heinz_, Jul 09 2014

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)