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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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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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COMMENTS
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Denominators are given under A120783.
From the expansion of sqrt(6)/3 = sqrt(1-1/3) = 1-(1/6)*Sum_{k=0..infinity} C(k)/12^k 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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FORMULA
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a(n) = numerator(r(n)), with the rationals r(n) = Sum_{k=0..n} C(k)/12^k 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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PROG
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(PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = numerator(sum(k=0, n, C(k)/12^k)); \\ Michel Marcus, Mar 02 2016
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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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