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A245006 Number of standard Young tableaux with n cells and 8 as last value in the first row. 2
232, 582, 1563, 4384, 12939, 39198, 123629, 398003, 1324715, 4489759, 15653882, 55503161, 201686249, 744669554, 2809714695, 10764956657, 42053547589, 166724084605, 672761983296, 2753474296366, 11453358056417, 48292313841411, 206690703254636, 896160453214130 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified May 28 16:37 EDT 2022. Contains 354119 sequences. (Running on oeis4.)