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Search: id:A120778
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| A120778 |
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Numerators of partial sums of Catalan numbers scaled by powers of 1/4. |
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+0
5
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| 1, 5, 11, 93, 193, 793, 1619, 26333, 53381, 215955, 436109, 3518265, 7088533, 28539857, 57414019, 1846943453, 3711565741, 14911085359, 29941580393, 240416274739, 482473579583, 1936010885087, 3883457090629
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For denominators see A120777.
From the expansion of 0 = sqrt(1-1) = 1-(1/2)*sum(C(k)/4^k,k=0..infinity) one has r:=limit(r(n),n to infinity)=2, with the partial sums r(n) defined below.
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LINKS
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W. Lang: Rationals r(n) and limit 2.
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FORMULA
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a(n)=numerator(r(n)), with the rationals r(n):=sum(C(k)/4^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
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EXAMPLE
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Rationals r(n): [1, 5/4, 11/8, 93/64, 193/128, 793/512, 1619/1024, 26333/16384,...].
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CROSSREFS
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Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)
Factor of A160481.
(End)
Adjacent sequences: A120775 A120776 A120777 this_sequence A120779 A120780 A120781
Sequence in context: A057726 A057727 A128454 this_sequence A042761 A123025 A053778
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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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