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Search: id:A120780
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| A120780 |
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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, 9, 37, 597, 2395, 19181, 76757, 2456653, 9827327, 78621047, 314488387, 5031843585, 20127426343, 161019596469, 644078720181, 41221047786429, 164884208824551, 1319073735418803, 5276295061084887, 84420721860989787
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Denominators are under A120781.
From the expansion of sqrt(2)/2 = sqrt(1-1/2) = 1-(1/4)*sum(C(k)/8^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 2*(2 - sqrt(2)) = 1.171572875..., with the partial sums r(n) defined below.
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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(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, 9/8, 37/32, 597/512, 2395/2048, 19181/16384,
76757/65536, 2456653/2097152,...].
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CROSSREFS
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Sequence in context: A026686 A076174 A117085 this_sequence A071229 A071238 A050854
Adjacent sequences: A120777 A120778 A120779 this_sequence A120781 A120782 A120783
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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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