A214801 Number of solid standard Young tableaux of shape [[2*n,n],[n]].

1, 6, 174, 7020, 325590, 16290708, 854630476, 46305862488, 2568272967270, 144984584562180, 8298621602461476, 480298712286979560, 28052543639835133692, 1650956086756046986440, 97790578929910135588440, 5824509559447044190027952, 348581174512709008160833158

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..555

S. B. Ekhad, D. Zeilberger, Computational and Theoretical Challenges on Counting Solid Standard Young Tableaux, arXiv:1202.6229v1 [math.CO], 2012

Wikipedia, Young tableau

Formula

Recurrence: (n-1)*n^2*(2*n-1)*(2*n+1)*(4*n-1)*(4*n+1)*(392*n^4 - 2044*n^3 + 4216*n^2 - 3944*n + 1377)*a(n) = 2*(n-1)*(1859648*n^10 - 13670048*n^9 + 43255264*n^8 - 75152192*n^7 + 75863336*n^6 - 41825576*n^5 + 7317576*n^4 + 5067372*n^3 - 3441344*n^2 + 785094*n - 59535)*a(n-1) - 4*(2*n-3)*(4*n-7)*(4*n-5)*(1310848*n^8 - 7998592*n^7 + 19695952*n^6 - 24269488*n^5 + 15125236*n^4 - 3514192*n^3 - 1066614*n^2 + 533457*n - 45927)*a(n-2) + 5184*n*(2*n-5)*(2*n-3)*(4*n-11)*(4*n-9)*(4*n-7)*(4*n-5)*(392*n^4 - 476*n^3 + 436*n^2 - 76*n - 3)*a(n-3). - Vaclav Kotesovec, Aug 31 2014

a(n) ~ sqrt((5*sqrt(5)-11)/4) * 64^n / (Pi*n). - Vaclav Kotesovec, Aug 31 2014

Maple

b:= proc(x, y, z) option remember; `if`(z>y, b(x, z, y),
      `if`({x, y, z}={0}, 1, `if`(x>y 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(2*n, n, n):
seq(a(n), n=0..20);

Mathematica

b[x_, y_, z_] := b[x, y, z] = If[z>y, b[x, z, y], If[Union[{x, y, z}] == {0}, 1, If[x>y && 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[2n, n, n]; Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Feb 05 2015, after Alois P. Heinz *)

Crossrefs

Central row elements of A214775.

Column k=2 of A176129.

Sequence in context: A317795 A166762 A323279 * A233225 A055165 A318538

Adjacent sequences: A214798 A214799 A214800 * A214802 A214803 A214804

Keyword

nonn

Author

Alois P. Heinz, Jul 28 2012

Status

approved