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%I #12 Feb 08 2017 18:36:30
%S 0,429,62016,807300,5101360,21732542,71916768,199448964,485325150,
%T 1067658735,2167714560,4122884232,7427426292,12781794760,21151379600,
%U 33835482648,52547352546,79506102225,117541332480,170211285180,241935349656,338141745810,465431207488
%N Number of standard Young tableaux of shape [7n,7].
%C Also the number of binary words with 7n 1's and 7 0's such that for every prefix the number of 1's is >= the number of 0's.
%H Alois P. Heinz, <a href="/A215547/b215547.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>
%F G.f.: (6*x^7 -48*x^6 +2808*x^5 +83196*x^4 +355384*x^3 +323184*x^2 +58584*x +429)*x / (x-1)^8.
%F a(n) = C(7*n+7,7)*(7*n-6)/(7*n+1) for n>0, a(0) = 0.
%p a:= n-> max(0, binomial(7*n+7,7)*(7*n-6)/(7*n+1)):
%p seq(a(n), n=0..30);
%t Join[{0},Table[Binomial[7n+7,7] (7n-6)/(7n+1),{n,30}]] (* _Harvey P. Dale_, Jul 24 2016 *)
%Y Row n=7 of A214776.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Aug 16 2012
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