A210427 - OEIS

%I #22 Sep 20 2020 13:36:59

%S 0,1,12,69,260,751,1812,3843,7400,13221,22252,35673,54924,81731,

%T 118132,166503,229584,310505,412812,540493,698004,890295,1122836,

%U 1401643,1733304,2125005,2584556,3120417,3741724,4458315,5280756,6220367,7289248,8500305,9867276

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

%H Bruno Berselli, <a href="/A210427/b210427.txt">Table of n, a(n) for n = 0..1000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

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

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

%p a:= n-> n*(12+(35+13*n^2)*n^2)/60:

%p seq(a(n), n=0..40);

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

%Y Row n=5 of A210391.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Mar 21 2012