%I #19 Feb 08 2017 19:21:05

%S 0,1,36,630,6512,45628,239316,1007083,3570240,11042199,30569012,

%T 77221232,180646896,395884866,820217412,1618520277,3060257024,

%U 5572071725,9810869508,16763347626,27879160048,45246275592,71818632820,111707913791,170553162816,255984075075

%N Number of semistandard Young tableaux over all partitions of 10 with maximal element <= n.

%H Bruno Berselli, <a href="/A210432/b210432.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_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

%F a(n) = n^2*(126432+(206020+(101031+(18930+1187*n^2)*n^2)*n^2)*n^2)/453600.

%F G.f.: -x*(x+1)*(x^8 +24*x^7 +265*x^6 +1132*x^5 +1904*x^4 +1132*x^3 +265*x^2 +24*x+1) / (x-1)^11.

%p a:= n-> n^2* (126432+ (206020+ (101031+ (18930+ 1187*n^2) *n^2) *n^2) *n^2)/ 453600:

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

%Y Row n=10 of A210391.

%K nonn,easy

%O 0,3

%A _Alois P. Heinz_, Mar 21 2012