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Search: id:A120789
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| A120789 |
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Numerators of partial sums of Catalan numbers scaled by powers of -1/8. |
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+0
2
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| 1, 7, 29, 459, 1843, 14723, 58925, 1885171, 7541399, 60328761, 241319243, 3861078495, 15444365983, 123554742139, 494219302861, 31630025688259, 126520120431871, 1012160898632573, 4048643713939967, 64778298539407877
(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(3/2) = 1+(1/4)*sum(C(k)/(-8)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= 2*(sqrt(6)-2)) = 0.898979485...
Denominators are given under A120781 (but may differ for higher n values).
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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)/8^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, 7/8, 29/32, 459/512, 1843/2048, 14723/16384,
58925/65536, 1885171/2097152, 7541399/8388608,...].
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CROSSREFS
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Sequence in context: A126394 A074468 A071918 this_sequence A135629 A122119 A157422
Adjacent sequences: A120786 A120787 A120788 this_sequence A120790 A120791 A120792
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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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