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Search: id:A120999
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| A120999 |
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Denominators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49. |
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2
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| 1, 49, 2401, 117649, 823543, 40353607, 13841287201, 678223072849, 33232930569601, 1628413597910449, 79792266297612001, 558545864083284007, 27368747340080916343, 9387480337647754305649, 459986536544739960976801
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Numerators are given under A120998.
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).
See A120998 for more details and a W. Lang link there for the definition of four p-families of such scaled Catalan sums.
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FORMULA
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a(n)=denominator(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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Adjacent sequences: A120996 A120997 A120998 this_sequence A121000 A121001 A121002
Sequence in context: A065785 A061615 A049682 this_sequence A087752 A069741 A099367
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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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