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Search: id:A121003
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| A121003 |
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Denominators of partial sums of Catalan numbers scaled by powers of 1/5. |
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+0
2
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| 1, 5, 25, 25, 625, 3125, 15625, 78125, 3125, 1953125, 9765625, 48828125, 244140625, 244140625, 1220703125, 6103515625, 30517578125, 152587890625, 152587890625, 3814697265625, 19073486328125
(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 A121002.
This is the first member (p=0) of the second p-family of partial sums of normalized scaled Catalan series CsnII(p):=sum(C(k)/((5^k)*F(2*p+1)^(2*k)),k=0..infinity) with limit F(2*p+1)*(L(2*p+2) - L(2*p+1)*phi) = F(2*p+1)*sqrt(5)/phi^(2*p+1), with C(n)=A000108(n) (Catalan), F(n)= A000045(n) (Fibonacci), L(n) = A000032(n) (Lucas) and phi:=(1+sqrt(5))/2 (golden section).
For more details on this p-family and the other three ones see the W. Lang links under A120996 and A121002.
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FORMULA
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a(n)=denominator(r(n)) with r(n) := rII(p=0,n) = sum(C(k)/5^k,k=0..n), 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, 6/5, 32/25, 33/25, 839/625, 4237/3125,
21317/15625, 107014/78125, 4292/3125, 2687362/1953125,...].
A120787 (denominators, second member p=1).
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CROSSREFS
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Sequence in context: A070382 A039936 A124398 this_sequence A121007 A043057 A137112
Adjacent sequences: A121000 A121001 A121002 this_sequence A121004 A121005 A121006
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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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