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Search: id:A101850
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| A101850 |
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A Catalan transform of Pell(n+1). |
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+0
3
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| 1, 2, 7, 26, 100, 392, 1555, 6218, 25006, 100988, 409162, 1661948, 6764194, 27575732, 112570675, 460058906, 1881978694, 7704907724, 31566153058, 129400608044, 530734613920, 2177792579072, 8939838222718, 36711025334948
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A Catalan transform of the Pell numbers A000129(n+1) under the mapping G(x)-> G(xc(x)), c(x) the g.f. of A000108. The inverse mapping is H(x)->H(x(1-x)).
Hankel transform is 3^n. [From Paul Barry (pbarry(AT)wit.ie), Jan 19 2009]
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FORMULA
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G.f.: 2/(3sqrt(1-4x)+2x-1); a(n)=sum{k=0..n, (k/(2n-k))binomial(2n-k, n-k)A000129(k+1)}.
a(n)=Sum_{k, 0<=k<=n} A039599(n,k)*A016116(k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 29 2008]
G.f.: 1/(1-2x-3x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-2x-x^2/(1-... (continued fraction). [From Paul Barry (pbarry(AT)wit.ie), Jan 19 2009]
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CROSSREFS
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Cf. A081696, A026641.
Sequence in context: A126223 A114121 A049775 this_sequence A045868 A129482 A150536
Adjacent sequences: A101847 A101848 A101849 this_sequence A101851 A101852 A101853
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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), Dec 18 2004
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