A210428 - OEIS

%I #17 Feb 08 2017 19:19:38

%S 0,1,16,119,560,1955,5552,13573,29632,59229,110320,193963,325040,

%T 523055,813008,1226345,1801984,2587417,3639888,5027647,6831280,

%U 9145115,12078704,15758381,20328896,25955125,32823856,41145651,51156784,63121255,77332880,94117457

%N Number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.

%C a(n) is the number of semistandard Young tableaux over all partitions of 6 with maximal element <= n.

%H Bruno Berselli, <a href="/A210428/b210428.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_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = n^2*(76+(85+19*n^2)*n^2)/180.

%F G.f.: -x*(x+1)*(x^4+8*x^3+20*x^2+8*x+1)/(x-1)^7.

%p a:= n-> n^2*(76+(85+19*n^2)*n^2)/180:

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

%Y Row n=6 of A210391.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Mar 21 2012