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Search: id:A120791
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| A120791 |
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Numerators of partial sums of Catalan numbers scaled by powers of -1/20. |
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+0
2
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| 1, 19, 191, 1527, 76357, 1527119, 15271223, 1221697411, 488678993, 244339494069, 2443394944889, 97735797766167, 977357977713673, 3909431910817547, 39094319108242331, 6255091057316833991
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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From the expansion of sqrt(1+1/5) = 1+(1/10)*sum(C(k)/(-20)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= (2*(sqrt(30)-5)) = 0.954451150....
Denominators are given under A120796.
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LINKS
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W. Lang: Rationals r(n) and limit.
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FORMULA
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a(n)=numerator(r(n)), with the rationals r(n):=sum(((-1)^k)*C(k)/20^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, 19/20, 191/200, 1527/1600, 76357/80000,
1527119/1600000, 15271223/16000000, 1221697411/1280000000,...]
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CROSSREFS
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Sequence in context: A142268 A107695 A005759 this_sequence A048556 A141995 A097445
Adjacent sequences: A120788 A120789 A120790 this_sequence A120792 A120793 A120794
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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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