A245007 Number of standard Young tableaux with n cells and 9 as last value in the first row.

764, 2031, 5741, 17088, 52540, 168172, 551142, 1866639, 6448956, 22908742, 82853921, 306971909, 1156564466, 4451496217, 17407985332, 69394132575, 280851149296, 1156692921549, 4833132867603, 20521962586186, 88343703440840, 386014928037316, 1708872377386105

Offset

9,1

Comments

Also the number of ballot sequences of length n where 9 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 = 9..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, 9]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 9, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=9 of A238794.

Sequence in context: A121321 A084072 A049534 * A204356 A238920 A054468

Adjacent sequences: A245004 A245005 A245006 * A245008 A245009 A245010

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved