A245003 Number of standard Young tableaux with n cells and 5 as last value in the first row.

10, 19, 41, 96, 232, 596, 1561, 4283, 11946, 34605, 101789, 309370, 954184, 3030085, 9758279, 32256938, 108044358, 370368959, 1285265155, 4552197618, 16308951180, 59495863566, 219423534749, 822464523053, 3115612818090, 11977083593001, 46520790003111

Offset

5,1

Comments

Also the number of ballot sequences of length n where 5 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 = 5..100

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, 5]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 5, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=5 of A238794.

Sequence in context: A195955 A127194 A083705 * A298487 A359315 A082659

Adjacent sequences: A245000 A245001 A245002 * A245004 A245005 A245006

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved