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A245007 Number of standard Young tableaux with n cells and 9 as last value in the first row. 2
764, 2031, 5741, 17088, 52540, 168172, 551142, 1866639, 6448956, 22908742, 82853921, 306971909, 1156564466, 4451496217, 17407985332, 69394132575, 280851149296, 1156692921549, 4833132867603, 20521962586186, 88343703440840, 386014928037316, 1708872377386105 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 3 07:58 EDT 2021. Contains 346435 sequences. (Running on oeis4.)