A245008 Number of standard Young tableaux with n cells and 10 as last value in the first row.

2620, 7408, 22088, 68576, 221715, 736624, 2528896, 8873588, 32006883, 117678413, 443117232, 1698040262, 6645905493, 26440507207, 107212883073, 441495784378, 1849869784105, 7864963647493, 33977806366991, 148834877695923, 661707905560864, 2980829993379396

Offset

10,1

Comments

Also the number of ballot sequences of length n where 10 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 = 10..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, 10]; Table[Print["a(", n, ") = ", an = a[n]]; an, {n, 10, 40}] (* Jean-François Alcover, Feb 06 2015, after Maple code in A238794 *)

Crossrefs

Column k=10 of A238794.

Sequence in context: A252440 A066871 A180650 * A180330 A238921 A156398

Adjacent sequences: A245005 A245006 A245007 * A245009 A245010 A245011

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jul 09 2014

Status

approved