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Search: id:A097331
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| A097331 |
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Expansion of 1+2x/(1+sqrt(1-4x^2)). |
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+0
8
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| 1, 1, 0, 1, 0, 2, 0, 5, 0, 14, 0, 42, 0, 132, 0, 429, 0, 1430, 0, 4862, 0, 16796, 0, 58786, 0, 208012, 0, 742900, 0, 2674440, 0, 9694845, 0, 35357670, 0, 129644790, 0, 477638700, 0, 1767263190, 0, 6564120420, 0, 24466267020, 0, 91482563640, 0, 343059613650, 0
(list; graph; listen)
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OFFSET
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0,6
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COMMENT
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Binomial transform is A097332. Second binomial transform is A014318.
Essentially the same as A126120. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 15 2008
Hankel transform is A087960(n)=(-1)^binomial(n+1,2). [From Paul Barry (pbarry(AT)wit.ie), Aug 10 2009]
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FORMULA
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a(n)=0^n+Catalan((n-1)/2)(1-(-1)^n)/2
Unsigned version of A090192, A105523 . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 29 2006
Contribution from Paul Barry (pbarry(AT)wit.ie), Aug 10 2009: (Start)
G.f.: 1+xc(x^2), c(x) the g.f. of A000108;
G.f.: 1/(1-x/(1+x/(1+x/(1-x/(1-x/(1+x/(1+x/(1-x/(1-x/(1+... (continued fraction);
G.f.: 1+x/(1-x^2/(1-x^2/(1-x^2/(1-x^2/(1-... (continued fraction). (End)
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CROSSREFS
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Sequence in context: A105523 A126120 A090192 this_sequence A094032 A117780 A155759
Adjacent sequences: A097328 A097329 A097330 this_sequence A097332 A097333 A097334
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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), Aug 05 2004
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