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Search: id:A120784
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| A120784 |
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Numerators of partial sums of Catalan numbers scaled by powers of 1/16. |
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+0
2
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| 1, 17, 137, 4389, 35119, 561925, 4495433, 287708141, 2301665843, 36826655919, 294613251551, 9427624079025, 75420992684203, 1206735883132973, 9653887065398089, 1235697544380650237
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OFFSET
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0,2
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COMMENT
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Denominators are given under A120785.
From the expansion of sqrt(3)/2 = sqrt(1-1/4) = 1-(1/8)*sum(C(k)/16^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 4*(2 - sqrt(3)) = 1.071796769..., with the partial sums r(n) defined below.
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LINKS
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W. Lang: Rationals r(n) and limit.
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FORMULA
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a(n)=numerator(r(n)), with the rationals r(n):=sum(C(k)/16^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.
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EXAMPLE
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Rationals r(n): [1, 17/16, 137/128, 4389/4096, 35119/32768, 561925/524288, 4495433/4194304, 287708141/268435456,...].
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CROSSREFS
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Sequence in context: A041550 A142788 A085958 this_sequence A099922 A142815 A008417
Adjacent sequences: A120781 A120782 A120783 this_sequence A120785 A120786 A120787
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 20 2006
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