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%I #14 Oct 23 2020 06:40:35
%S 1,140,79380,62563200,57288340200,57169180452384,60324072262534080,
%T 66193973824733314560,74770747698820830356700,
%U 86365239335124673905181200,101541339191092781603799640464
%N a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+2)*(7k+5).
%H G. C. Greubel, <a href="/A185402/b185402.txt">Table of n, a(n) for n = 0..320</a>
%F Self-convolution of A185401:
%F A185401(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+2)*(14k+5).
%F a(n) ~ cos(3*Pi/14) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - _Vaclav Kotesovec_, Oct 23 2020
%e G.f.: A(x) = 1 + 140*x + 79380*x^2 + 62563200*x^3 +...
%e A(x)^(1/2) = 1 + 70*x + 37240*x^2 + 28674800*x^3 +...+ A185401(n)*x^n +...
%t Table[Binomial[2n,n] 7^n/(n!)^2 Product[(7k+2)(7k+5),{k,0,n-1}],{n,0,10}] (* _Harvey P. Dale_, May 10 2012 *)
%o (PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0,n-1,(7*k+2)*(7*k+5))}
%Y Cf. A184896, A185401, A185404.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 26 2011
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