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A245005 Number of standard Young tableaux with n cells and 7 as last value in the first row. 2
76, 176, 441, 1181, 3264, 9484, 28152, 87000, 273765, 891072, 2948867, 10045602, 34762462, 123358872, 444384780, 1636678431, 6116179699, 23312140822, 90119096883, 354665480523, 1415057313215, 5738879374046, 23584547598278, 98391428094200, 415716316206635 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,1

COMMENTS

Also the number of ballot sequences of length n where 7 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 = 7..75

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, 7]; Table[Print["a(", n, ") = ", an = a[n]]; an , {n, 7, 40}] (* Jean-Fran├žois Alcover, Feb 06 2015, after Maple code in A238794 *)

CROSSREFS

Column k=7 of A238794.

Sequence in context: A099944 A044408 A044789 * A138855 A324632 A251078

Adjacent sequences:  A245002 A245003 A245004 * A245006 A245007 A245008

KEYWORD

nonn

AUTHOR

Joerg Arndt and Alois P. Heinz, Jul 09 2014

STATUS

approved

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Last modified November 20 20:46 EST 2019. Contains 329347 sequences. (Running on oeis4.)