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A210427
Number of semistandard Young tableaux over all partitions of 5 with maximal element <= n.
2
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
0,3
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.
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 *)
CROSSREFS
Row n=5 of A210391.
Sequence in context: A238536 A096425 A212753 * A101097 A067702 A163193
KEYWORD
nonn,easy
AUTHOR
Alois P. Heinz, Mar 21 2012
STATUS
approved