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Search: id:A120998
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| A120998 |
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Numerators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49. |
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3
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| 1, 50, 2452, 120153, 841073, 41212583, 14135916101, 692659889378, 33940334580952, 1663076394471510, 81490743329120786, 570435203303853900, 27951324961888870816, 9587304461927883432788, 469777918634466290881052
(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 given under A120999.
This is the third member (p=2) of the first p-family of partial sums of normalized scaled Catalan series CsnI(p):=sum(C(k)/L(2*p)^(2*k),k=0..infinity) with limit L(2*p)*(F(2*p+1) - F(2*p)*phi) = L(2*p)/phi^(2*p), with C(n)=A000108(n) (Catalan), F(n)= A000045(n) (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden section).
The partial sums of the above mentioned first p-family are rI(p;n):=sum(C(k)/L(2*p)^(2*k),k=0..n), n>=0, for p=0,1,...
For more details on this p-family and the other three ones see the W. Lang link under A120996.
The limit lim_{n->infinity} r(n) = 7*(5 - 3* phi) = 7/phi^4 = 1.0212862362522 (maple10, 15 digits).
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LINKS
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W. Lang: Rationals r(n), limit.
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FORMULA
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a(n)=numerator(r(n)) with r(n) := rI(p=2,n) = sum(C(k)/L(4)^(2*k),k=0..n), with Lucas L(4)=7 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.
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EXAMPLE
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Rationals r(n): [1, 50/49, 2452/2401, 120153/117649, 841073/823543,
41212583/40353607, 14135916101/13841287201,...].
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CROSSREFS
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Sequence in context: A164986 A156087 A078304 this_sequence A165800 A042201 A097838
Adjacent sequences: A120995 A120996 A120997 this_sequence A120999 A121000 A121001
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
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