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A121001
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Denominators of partial sums of Catalan numbers scaled by powers of 1/18^2 = 1/324.
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1
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1, 324, 52488, 34012224, 5509980288, 595077871104, 96402615118848, 124937789194027008, 60719765548297125888, 19673204037648268787712, 3187059054099019543609344, 2065214267056164664258854912
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OFFSET
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0,2
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COMMENTS
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Numerators are given under A121000.
This is the fourth member (p=3) 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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LINKS
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FORMULA
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a(n)=denominator(r(n)) with r(n) := rI(p=3,n) = sum(C(k)/L(6)^(2*k),k=0..n), with Lucas L(6)=18 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, 325/324, 52651/52488, 34117853/34012224, 5527092193/5509980288, 596925956851/595077871104, ...].
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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