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A219013
Denominators in a product expansion for sqrt(3).
4
11, 523451, 39571031999225940638473470251
OFFSET
0,1
COMMENTS
The product expansion in question is sqrt(3) = product {n = 0..inf} (1 + 2*A219012(n)/A219013(n)) = (1 + 2*4/11)*(1 + 2*724/523451)*(1 + 2*198924689265124/39571031999225940638473470251)*....
FORMULA
Let alpha = 1/2*(sqrt(2) + sqrt(6)) and put f(n) = 1/sqrt(6)*{alpha^n - (-1/alpha)^n}. Then a(n) = f(5^(n+1))/f(5^n).
a(n) = A219012(n)^2 - A219012(n) - 1.
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) = 11.
CROSSREFS
KEYWORD
nonn,easy,bref
AUTHOR
Peter Bala, Nov 09 2012
STATUS
approved