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A210429 Number of semistandard Young tableaux over all partitions of 7 with maximal element <= n.

%I A210429 #19 Jan 29 2023 13:51:52
%S A210429 0,1,20,189,1100,4615,15372,43219,106808,238581,491380,946913,1726308,
%T A210429 3002987,5018092,8098695,12679024,19324937,28761876,41906533,59902460,
%U A210429 84159855,116399756,158702875,213563304,283947325,373357556,485902665,626372884,800321555
%N A210429 Number of semistandard Young tableaux over all partitions of 7 with maximal element <= n.
%H A210429 Bruno Berselli, <a href="/A210429/b210429.txt">Table of n, a(n) for n = 0..1000</a>
%H A210429 Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%H A210429 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F A210429 a(n) = n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260.
%F A210429 G.f.: x*(x+1)^2*(x^4+10*x^3+36*x^2+10*x+1)/(x-1)^8.
%p A210429 a:= n-> n*(180+(637+(385+58*n^2)*n^2)*n^2)/1260:
%p A210429 seq(a(n), n=0..40);
%t A210429 CoefficientList[Series[x (x+1)^2(x^4+10x^3+36x^2+10x+1)/(x-1)^8,{x,0,40}],x] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{0,1,20,189,1100,4615,15372,43219},40] (* _Harvey P. Dale_, Jan 29 2023 *)
%Y A210429 Row n=7 of A210391.
%K A210429 nonn,easy
%O A210429 0,3
%A A210429 _Alois P. Heinz_, Mar 21 2012