A210427 Number of semistandard Young tableaux over all partitions of 5 with maximal element <= n.

0, 1, 12, 69, 260, 751, 1812, 3843, 7400, 13221, 22252, 35673, 54924, 81731, 118132, 166503, 229584, 310505, 412812, 540493, 698004, 890295, 1122836, 1401643, 1733304, 2125005, 2584556, 3120417, 3741724, 4458315, 5280756, 6220367, 7289248, 8500305, 9867276

Offset: 0

Author

Alois P. Heinz, Mar 21 2012

Keywords

• nonn
• easy

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Wikipedia, Young tableau
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Row n=5 of A210391.

Programs

Maple

a:= n-> n*(12+(35+13*n^2)*n^2)/60:
seq(a(n), n=0..40);

Mathematica

LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,12,69,260,751},40] (* Harvey P. Dale, Sep 20 2020 *)

Formula

a(n) = n*(12+(35+13*n^2)*n^2)/60.

G.f.: x*(12*x^2+6*x^3+x^4+1+6*x)/(x-1)^6.