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A245008 Number of standard Young tableaux with n cells and 10 as last value in the first row. 2
2620, 7408, 22088, 68576, 221715, 736624, 2528896, 8873588, 32006883, 117678413, 443117232, 1698040262, 6645905493, 26440507207, 107212883073, 441495784378, 1849869784105, 7864963647493, 33977806366991, 148834877695923, 661707905560864, 2980829993379396 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified January 18 00:48 EST 2022. Contains 350410 sequences. (Running on oeis4.)