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A195600
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Continued fraction for beta = 3/(2*log(alpha/2)); alpha = A195596.
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7
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1, 1, 20, 3, 2, 7, 1, 1, 1, 12, 1, 5, 1, 91, 1, 1, 3, 87, 2, 1, 1, 1, 1, 3, 1, 9, 3, 2, 1, 1, 1, 1, 190, 1, 3, 1, 82, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 2, 12, 6, 2, 2, 2, 3, 2, 1, 1, 1, 2, 3, 21, 1, 1, 12, 1, 7, 3, 2, 26, 3, 2, 1, 1, 1, 9, 1, 15, 4, 3, 3, 1, 3, 1
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OFFSET
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0,3
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COMMENTS
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beta is used to measure the expected height of random binary search trees.
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LINKS
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FORMULA
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beta = 3/(2*log(alpha/2)) = 3*alpha/(2*alpha-2), where alpha = A195596 = -1/W(-exp(-1)/2) and W is the Lambert W function.
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EXAMPLE
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1.95302570335815413945406288542575380414251340201036319609354...
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MAPLE
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with(numtheory):
alpha:= solve(alpha*log((2*exp(1))/alpha)=1, alpha):
beta:= 3/(2*log(alpha/2)):
cfrac(evalf(beta, 130), 100, 'quotients')[];
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MATHEMATICA
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beta = 3/(2+2*ProductLog[-1/(2*E)]); ContinuedFraction[beta, 83] (* Jean-François Alcover, Jun 20 2013 *)
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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