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%I #10 Oct 23 2020 06:32:48
%S 1,84,45864,35672000,32445913500,32247604076688,33935228690034672,
%T 37165308416775931392,41919854708375196052500,
%U 48365506771435816732770000,56812832722107710740048677120,67715433011522917282547695380480
%N a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+1)*(7k+6).
%F Self-convolution of A184895, where A184895(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+1)*(14k+6).
%F a(n) ~ sin(Pi/7) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - _Vaclav Kotesovec_, Oct 23 2020
%e G.f.: A(x) = 1 + 84*x + 45864*x^2 + 35672000*x^3 +...
%e A(x)^(1/2) = 1 + 42*x + 22050*x^2 + 16909900*x^3 +...+ A184895(n)*x^n +...
%o (PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0,n-1,(7*k+1)*(7*k+6))}
%Y Cf. A184895; variants: A184423, A008977, A184892, A001421, A184898.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 25 2011
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