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Search: id:A120782
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| A120782 |
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Numerators of partial sums of Catalan numbers scaled by powers of 1/12. |
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+0
2
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| 1, 13, 79, 1901, 11413, 45659, 273965, 13150463, 236709049, 2840511019, 17043070313, 409033716905, 2454202353433, 29450428426921, 58900856965277, 1884827423966069, 11308964545760729, 407122723668993709
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OFFSET
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0,2
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COMMENT
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Denominators are given under A120783.
From the expansion of sqrt(6)/3 = sqrt(1-1/3) = 1-(1/6)*sum(C(k)/12^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 2*(3 - sqrt(6)) = 1.101020514..., 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)/12^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, 13/12, 79/72, 1901/1728, 11413/10368,
45659/41472, 273965/248832, 13150463/11943936,...].
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CROSSREFS
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Adjacent sequences: A120779 A120780 A120781 this_sequence A120783 A120784 A120785
Sequence in context: A075584 A126481 A032625 this_sequence A032652 A136373 A071614
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KEYWORD
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nonn,easy
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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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