From Peter Bala, Nov 12 2012: (Start)
a(n) = alpha^(2^(n-1)) + (1/alpha)^(2^(n-1)) - 1, where alpha := 1/2*(5 + sqrt(21)).
Recurrence: a(n) = 6*{product {k = 1..n-1} a(k)} - 2 with a(1) = 4.
Product {n = 1..inf} (1 + 1/a(n)) = 2/7*sqrt(21).
Product {n = 1..inf} (1 + 2/(a(n) + 1)) = sqrt(7/3).
(End)
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