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A120783
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Denominators of partial sums of Catalan numbers scaled by powers of 1/12.
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5
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1, 12, 72, 1728, 10368, 41472, 248832, 11943936, 214990848, 2579890176, 15479341056, 371504185344, 2229025112064, 26748301344768, 53496602689536, 1711891286065152, 10271347716390912, 369768517790072832
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OFFSET
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0,2
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COMMENTS
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Numerators are given under A120782.
It appears that the terms of this sequence are denominators of the power series expansion of 1+sqrt(x) at x=3, scaled by 1/(2*sqrt(3)). - Alexander R. Povolotsky, Mar 01 2016
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LINKS
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FORMULA
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a(n) = denominator(r(n)), with the rationals r(n) = Sum_{k=0..n} C(k)/12^k with C(k) = A000108(k) (Catalan numbers).
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MATHEMATICA
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Denominator@ Table[Sum[CatalanNumber@ k/12^k, {k, 0, n}], {n, 0, 17}] (* Michael De Vlieger, Mar 03 2016 *)
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PROG
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(PARI) C(n) = binomial(2*n, n)/(n+1); \\ A000108
a(n) = denominator(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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