A215687 Number of solid standard Young tableaux of shape [[2*n,2],[2]].

0, 16, 174, 690, 1876, 4140, 7986, 14014, 22920, 35496, 52630, 75306, 104604, 141700, 187866, 244470, 312976, 394944, 492030, 605986, 738660, 891996, 1068034, 1268910, 1496856, 1754200, 2043366, 2366874, 2727340, 3127476, 3570090, 4058086, 4594464, 5182320

Offset: 0

Author

Alois P. Heinz, Aug 20 2012

Keywords

• nonn
• easy

Links

• 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
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Row n=2 of A176129.

Programs

Maple

a:= n-> (-7+(7+(12+4*n)*n)*n)*n;
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{5,-10,10,-5,1},{0,16,174,690,1876},40] (* Harvey P. Dale, Jul 08 2017 *)

Formula

G.f.: 2*(3*x^3-10*x^2+47*x+8)*x/(1-x)^5.

a(n) = n*(2*n-1)*(2*n^2+7*n+7).