A245002 Number of standard Young tableaux with n cells and 4 as last value in the first row.

4, 7, 14, 29, 66, 152, 374, 933, 2440, 6476, 17812, 49700, 142806, 416028, 1244052, 3769709, 11701968, 36779876, 118196856, 384069992, 1272985450, 4258319604, 14489712986, 49658295960, 172626616246, 603254904952, 2132886737604, 7568733370478, 27115881832378

Offset

4,1

Comments

Also the number of ballot sequences of length n where 4 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 = 4..1000

Vaclav Kotesovec, Recurrence (of order 6)

Wikipedia, Young tableau

Formula

a(n) ~ 2^(2*n-3) / (Pi*n^3). - Vaclav Kotesovec, Aug 27 2014

Example

a(4) = 4:
[1 4]  [1 2 4]  [1 3 4]  [1 2 3 4]
[2]    [3]      [2]
[3]

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, 4] ; Table[Print["a(", n, ") = ", an = a[n]]; an, {n, 4, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=4 of A238794.

Sequence in context: A049946 A076975 A050343 * A199628 A049945 A234576

Adjacent sequences: A244999 A245000 A245001 * A245003 A245004 A245005

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved