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

232, 582, 1563, 4384, 12939, 39198, 123629, 398003, 1324715, 4489759, 15653882, 55503161, 201686249, 744669554, 2809714695, 10764956657, 42053547589, 166724084605, 672761983296, 2753474296366, 11453358056417, 48292313841411, 206690703254636, 896160453214130

Offset

8,1

Comments

Also the number of ballot sequences of length n where 8 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 = 8..50

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, 8]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 8, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=8 of A238794.

Sequence in context: A250645 A179246 A064715 * A252273 A153466 A200870

Adjacent sequences: A245003 A245004 A245005 * A245007 A245008 A245009

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved