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Search: id:A102898
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| A102898 |
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A Catalan related transform of 3^n. |
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+0
1
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| 1, 3, 9, 30, 99, 330, 1098, 3660, 12195, 40650, 135486, 451620, 1505358, 5017860, 16726068, 55753560, 185844771, 619482570, 2064940470, 6883134900, 22943778138, 76479260460, 254930851404, 849769504680, 2832564956814
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Transform of 1/(1-3x) under the mapping g(x)->g(xc(x^2)), where c(x) is the g.f. of the Catalan numbers A000108. The inverse transform is h(x)->h(x/(1+x^2)).
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REFERENCES
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Maria Paola Bonacina and Nachum Dershowitz, Canonical Inference for Implicational Systems, in Automated Reasoning, Lecture Notes in Computer Science, Volume 5195/2008, Springer-Verlag.
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FORMULA
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G.f.: 2x/(3sqrt(1-4x^2)+2x-3); a(0)=1, a(n)=sum{k=0..n, k*binomial(n-1, (n-k)/2)(1+(-1)^(n-k))3^k/(n+k)}, n>0.
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CROSSREFS
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Cf. A100087, A098615.
Sequence in context: A144817 A089978 A052906 this_sequence A050181 A089931 A148946
Adjacent sequences: A102895 A102896 A102897 this_sequence A102899 A102900 A102901
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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), Jan 17 2005
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