A245005 Number of standard Young tableaux with n cells and 7 as last value in the first row.

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

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-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=7 of A238794.

Sequence in context: A329542 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