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

0,2

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).

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).

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 *)

Crossrefs

Row n=2 of A176129.

Sequence in context: A021174 A021374 A253343 * A187720 A017931 A021129

Adjacent sequences: A215684 A215685 A215686 * A215688 A215689 A215690

Keyword

nonn,easy

Author

Alois P. Heinz, Aug 20 2012

Status

approved