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%I #15 Nov 01 2017 17:30:02
%S 1,9,170,3625,81510,1888460,44602348,1067658735,25810820750,
%T 628737007195,15408077648040,379444514503119,9382177773301060,
%U 232775087755980000,5792018711632340160,144481310070897555910,3611955405113118024990,90470699668284950782170
%N a(n) = binomial(10*n,n)*(8*n+1)/(9*n+1).
%C Number of standard Young tableaux of shape [9n,n].
%H Alois P. Heinz, <a href="/A215554/b215554.txt">Table of n, a(n) for n = 0..215</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F a(n) = C(10*n,n)*(8*n+1)/(9*n+1).
%F a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(8*n+1). - _Ilya Gutkovskiy_, Nov 01 2017
%p a:= n-> binomial(10*n,n)*(8*n+1)/(9*n+1):
%p seq(a(n), n=0..20);
%t Table[Binomial[10n,n] (8n+1)/(9n+1),{n,0,20}] (* _Harvey P. Dale_, Dec 19 2016 *)
%Y Column k=9 of A214776.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 15 2012
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