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A245003
Number of standard Young tableaux with n cells and 5 as last value in the first row.
2
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: A374806 A127194 A083705 * A372096 A298487 A359315
KEYWORD
nonn
AUTHOR
Joerg Arndt and Alois P. Heinz, Jul 09 2014
STATUS
approved