A210431 - OEIS

%I #19 Feb 08 2017 19:20:34

%S 0,1,30,434,3740,22220,100562,370909,1168008,3245311,8148590,18821968,

%T 40542228,82300842,158779362,293092635,520505744,893364637,1487517086,

%U 2410539918,3812130380,5897064040,8941168786,13310814265,19486468504,28090928475,39922889006

%N Number of semistandard Young tableaux over all partitions of 9 with maximal element <= n.

%H Bruno Berselli, <a href="/A210431/b210431.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_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n) = n*(10080+(40484+(31395+(8106+655*n^2)*n^2)*n^2)*n^2)/90720.

%F G.f.: x*(x^8+20*x^7+179*x^6+630*x^5+960*x^4+630*x^3+179*x^2+20*x+1) / (x-1)^10.

%p a:= n-> n*(10080+(40484+(31395+(8106+655*n^2)*n^2)*n^2)*n^2)/90720:

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

%Y Row n=9 of A210391.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Mar 21 2012