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Search: id:A103970
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| A103970 |
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Expansion of (1-sqrt(1-4x-12x^2))/(2x). |
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+0
1
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| 1, 4, 8, 32, 128, 576, 2688, 13056, 65024, 330752, 1710080, 8962048, 47497216, 254132224, 1370849280, 7447117824, 40707293184, 223731253248, 1235630948352, 6853893292032, 38166664839168, 213288826699776, 1195775593807872
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Image of c(x), the g.f. of the Catalan numbers A000108 under the mapping g(x)->(1+3x)g(x(1+3x)). In general, the image of the Catalan numbers under the mapping g(x)->(1+i*x)g(x(1+i*x)) is given by a(n)=sum{k=0..n, i^(n-k)C(k)C(k+1,n-k)}.
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FORMULA
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G.f. : (1-sqrt(1-4x(1+3x))/(2x); a(n)=sum{k=0..n, 3^(n-k)C(k)C(k+1, n-k)}.
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CROSSREFS
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Cf. A025227, A025229, A103971, A103972.
Sequence in context: A086344 A068205 A113479 this_sequence A034785 A075398 A072868
Adjacent sequences: A103967 A103968 A103969 this_sequence A103971 A103972 A103973
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 23 2005
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