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A225112
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Decimal expansion of integral of 1/binomial(2x,x) from x = 0 to infinity.
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0
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1, 2, 2, 1, 6, 6, 3, 8, 9, 9, 5, 0, 1, 3, 7, 1, 8, 3, 6, 0, 6, 9, 9, 7, 8, 9, 5, 1, 5, 1, 1, 5, 1, 8, 9, 7, 3, 3, 9, 7, 0, 4, 1, 0, 1, 8, 9, 9, 2, 9, 1, 7, 5, 1, 7, 6, 8, 0, 4, 9, 7, 2, 0, 8, 3, 3, 4, 9, 6, 2, 2, 7, 4, 6, 3, 7, 9, 5, 2, 0, 9, 8, 6, 2, 1, 3, 5, 1, 3, 2, 8, 4, 8, 8, 3, 1, 5, 4, 4, 1, 2, 5, 8
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OFFSET
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1,2
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COMMENTS
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The central binomial coefficient is extended to non-integer values via the Gamma function.
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LINKS
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FORMULA
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Integral(t = 0 .. infinity, 1/binomial(2t, t)).
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EXAMPLE
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1.221663899501...
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MATHEMATICA
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NIntegrate[1/Binomial[2 t, t], {t, 0, Infinity}]
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PROG
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(PARI)
cbin(x)=exp(lngamma(2*x+1)-2*lngamma(x+1));
intnum(t=0, [oo, log(4)], 1/cbin(t))
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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