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A121009
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Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*3^2) = 1/45.
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5
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1, 45, 2025, 18225, 4100625, 61509375, 2767921875, 124556484375, 672605015625, 756680642578125, 34050628916015625, 1532278301220703125, 68952523554931640625, 620572711994384765625, 3102863559971923828125
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Numerators are given under A121008.
This is the second member (p=2) of the third p-family of partial sums of normalized scaled Catalan series CsnIII(p):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..infinity) with limit F(2*p)*(-L(2*p+1) + L(2*p)*phi) = F(2*p)*sqrt(5)/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 third p-family are rIII(p;n):=sum(((-1)^k)*C(k)/((5^k)*F(2*p)^(2*k)),k=0..n), n>=0, for p=1,...
For more details on this p-family and the other three ones see the W. Lang link under A120996 and A121008.
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FORMULA
| a(n)=denominator(r(n)) with r(n) := rIII(p=2,n) = sum(((-1)^k)*C(k)/((5^k)*F(2*2)^(2*k)),k=0..n), with F(4)=3 and C(k):=A000108(k) (Catalan). The rationals r(n) are given in lowest terms.
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EXAMPLE
| Rationals r(n): [1, 44/45, 1982/2025, 17837/18225, 4013339/4100625,
60200071/61509375, 2709003239/2767921875,...].
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CROSSREFS
| The first member (p=1) is A121006/A121007.
Sequence in context: A170678 A170726 A170764 * A009989 A095658 A109941
Adjacent sequences: A121006 A121007 A121008 * A121010 A121011 A121012
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KEYWORD
| nonn,frac,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 16 2006
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