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%I #14 Feb 02 2018 21:18:34
%S 29,45232349,189482250299273866821980904657123150749
%N Denominators in a product expansion for sqrt(2).
%C a(3) has 192 digits and a(4) has 957 digits.
%C The product expansion in question is sqrt(2) = product {n = 0..inf} (1 + 2*A219014(n)/A219015(n)) = (1 + 2*6/29)*(1 + 2*6726/45232349)*....
%H Alois P. Heinz, <a href="/A219015/b219015.txt">Table of n, a(n) for n = 0..4</a>
%F a(n) = Pell(5^(n+1))/Pell(5^n), where Pell(n) = A000129(n).
%F Recurrence equation: a(n+1) = 5/2*(a(n)^4 - a(n)^2)*sqrt(4*a(n) + 5) + a(n)^5 + 15/2*a(n)^4 - 25/2*a(n)^2 + 5 with initial condition a(0) = 29.
%t Table[Fibonacci[5^(n+1),2]/Fibonacci[5^n,2], {n,0,5}] (* _G. C. Greubel_, Feb 02 2018 *)
%Y Cf. A000129, A219011, A219013, A219014.
%K nonn,easy,bref
%O 0,1
%A _Peter Bala_, Nov 09 2012