A245004 Number of standard Young tableaux with n cells and 6 as last value in the first row.

26, 56, 132, 327, 863, 2333, 6620, 19130, 57515, 175771, 555673, 1784015, 5899056, 19795308, 68163789, 238040835, 850372635, 3079156803, 11376375381, 42585665859, 162324759308, 626699226366, 2459686799702, 9775044096970, 39436677372291, 161037770577853

Offset

6,1

Comments

Also the number of ballot sequences of length n where 6 is the position of the last occurrence of the minimal value.

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..80

Wikipedia, Young tableau

Mathematica

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, 6]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 6, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=6 of A238794.

Sequence in context: A255020 A184839 A038848 * A161341 A038861 A277976

Adjacent sequences: A245001 A245002 A245003 * A245005 A245006 A245007

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved