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A121504
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Numerators of partial sums of a series used for the series of sqrt(2) + sqrt(3) involving Catalan numbers.
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1
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3, 53, 433, 13941, 111759, 1789509, 14320329, 916611309, 7333257267, 117334608047, 938685468127, 30038055403185, 240304869286059, 3844880951681069, 30759058568289097, 3937160132112061181
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| The corresponding denominators are A120785(n).
The limit of this series is 4*(4-(sqrt(2)+sqrt(3))) = 3.414942518 (maple10, 10 digits).
See A121503 for the geometric interpretation of sqrt(2)+sqrt(3) and a Popper reference.
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LINKS
| W. Lang: Rationals r(n), limit.
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FORMULA
| a(n)= numerator(r(n)) with r(n):= sum(C(k)*(1+2^(k+1))/16^k,k=0..n), n>=0, with C(k)=A000108(k) (Catalan numbers).
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EXAMPLE
| Rationals r(n): [3, 53/16, 433/128, 13941/4096, 111759/32768,
1789509/524288, 14320329/4194304, 916611309/268435456,...].
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CROSSREFS
| A121503/(4*A120785) are the partial sums of a series for sqrt(2)+sqrt(3).
Sequence in context: A141929 A036941 A113612 * A099665 A173802 A001279
Adjacent sequences: A121501 A121502 A121503 * A121505 A121506 A121507
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
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