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%I #14 Nov 01 2017 17:29:06
%S 1,7,104,1748,31000,566618,10559208,199448964,3804949176,73143988775,
%T 1414591812920,27492340515912,536480138597624,10504551860174120,
%U 206284010045343000,4061109502392133464,80126310234711780600,1583953257985260802200,31365436013686385802048
%N a(n) = binomial(8*n,n)*(6*n+1)/(7*n+1).
%C Number of standard Young tableaux of shape [7n,n].
%H Alois P. Heinz, <a href="/A215552/b215552.txt">Table of n, a(n) for n = 0..235</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Young_tableau">Young tableau</a>
%F a(n) = C(8*n,n)*(6*n+1)/(7*n+1).
%F a(n) = [x^n] ((1 - sqrt(1 - 4*x))/(2*x))^(6*n+1). - _Ilya Gutkovskiy_, Nov 01 2017
%p a:= n-> binomial(8*n,n)*(6*n+1)/(7*n+1):
%p seq(a(n), n=0..20);
%t Table[Binomial[8n,n] (6n+1)/(7n+1),{n,0,20}] (* _Harvey P. Dale_, Mar 30 2014 *)
%Y Column k=7 of A214776.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 15 2012
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