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A219013
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Denominators in a product expansion for sqrt(3).
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4
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OFFSET
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0,1
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COMMENTS
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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)*....
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LINKS
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FORMULA
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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).
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.
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CROSSREFS
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KEYWORD
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nonn,easy,bref
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AUTHOR
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STATUS
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approved
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