A215122 -id:A215122 - cp's OEIS frontend

A215123 Number of solid standard Young tableaux of shape [[n^2,n],[n]].

1, 2, 174, 52808, 31497284, 31113230148, 46190668836656, 96484621769643360, 270280816277448460968, 979042561410295182717884, 4456728497956906393963534248, 24916868994347706845906490576432, 167903137478620963997932010166057408

Offset: 0

Alois P. Heinz, Aug 03 2012

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..100
S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
Wikipedia, Young tableau

Central row elements of A215122.

Main diagonal of A176129.

b:= proc(x, y, z) option remember; `if`(zy and x>z, b(x-1, y, z), 0)+
      `if`(y>0, b(x, y-1, z), 0)+ `if`(z>0, b(x, y, z-1), 0)))
    end:
a:= n-> b(n^2, n, n):
seq(a(n), n=0..15);

$RecursionLimit = 1000; b[x_, y_, z_] :=  b[x, y, z] = If[zy && x>z, b[x-1, y, z], 0] + If[y>0, b[x, y-1, z], 0] + If[z>0, b[x, y, z-1], 0]]]; a[n_] := b[n^2, n, n]; Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)

a(n) ~ exp(2*n+2) * n^(2*n-1) / (2*Pi). - Vaclav Kotesovec, Jan 19 2015

A215124 Number of solid standard Young tableaux of shape [[(n-2)*2,2],[n-2]].

Original entry on oeis.org

0, 0, 0, 8, 174, 2084, 21025, 194064, 1694224, 14232672, 116228871, 928763000, 7294771770, 56497996620, 432520209420, 3278863236544, 24649138276800, 183964353480832, 1364323157872947, 10061883449658936, 73839952091271730, 539488089621673500

Offset: 0

Alois P. Heinz, Aug 03 2012

nonn

a(n) is odd if and only if n = 2*k and k >= 3 and k in { A118113 }.

Alois P. Heinz, Table of n, a(n) for n = 0..1000
S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012
Wikipedia, Young tableau

Column k=2 of A215122.

a:= proc(n) option remember; `if`(n<4, [0, 0, 0, 8][n+1],
      3*(n-1)*(3*n-8)*(3*n-10)*(937*n-486*n^2+81*n^3-576)*a(n-1)
      /(2*(n-2)^2*(2*n-3)*(2152*n-729*n^2+81*n^3-2080)))
    end:
seq(a(n), n=0..30);

Flatten[{0, 0, 0, 8, Table[3*(n-1) * (3*n-8) * (-576 + 937*n - 486*n^2 + 81*n^3) * (3*n-10)! / (2 * (n-4)! * (2*n-3)!), {n, 4, 20}]}] (* Vaclav Kotesovec, Sep 02 2014 *)

For n > 3, a(n) = 3*(n-1) * (3*n-8) * (-576 + 937*n - 486*n^2 + 81*n^3) * (3*n-10)! / (2 * (n-4)! * (2*n-3)!). - Vaclav Kotesovec, Sep 02 2014

cp's OEIS Frontend

A215123 Number of solid standard Young tableaux of shape [[n^2,n],[n]].

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