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Search: id:A120069
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| A120069 |
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Denominators of partial sums of a convergent series involving scaled Catalan numbers A000108. |
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+0
3
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| 1, 2, 16, 32, 128, 256, 4096, 8192, 32768, 65536, 524288, 1048576, 4194304, 8388608, 268435456, 536870912, 2147483648, 4294967296, 34359738368, 68719476736, 274877906944, 549755813888, 8796093022208
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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For the corresponding denominator sequence see A119951.
The series s:=sum(C(k)/2^(2*(k-1)),k=1..infty), with C(n):=A000108(n) (Catalan numbers) is convergent due to J. L. Raabe's criterion. The value for s is 4 (see A119951).
The asymptotics for C(n)/2^(2*(k-1)) is 4/(sqrt(Pi)*k^(3/2)) (see mathworld). The sum over the asymptotic values from k=1..infinity is (4/sqrt(Pi))*Zeta(3/2) = 5.895499840 (maple10, 10 digits).
The partial sums r(n):=sum(C(k)/2^(2*(k-1)),k=1..n) are rationals (written in lowest terms).
For the rationals r(n) see the W. Lang link under A119951.
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FORMULA
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a(n)=denominator(r(n)) with the rationals r(n) defined above.
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CROSSREFS
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Sequence in context: A109210 A056707 A069256 this_sequence A018975 A012696 A012392
Adjacent sequences: A120066 A120067 A120068 this_sequence A120070 A120071 A120072
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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