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A097331
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Expansion of 1+2x/(1+sqrt(1-4x^2)).
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9
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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; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| 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
| 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)
G.f. 1/(1-z/(1-z/(1-z/(...)))) where z=x/(1+2*x) (continued fraction); more generally g.f. C(x/(1+2*x)) where C(x) is the g.f. for the Catalan numbers (A000108). [Joerg Arndt, Mar 18 2011]
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MAPLE
| A097331_list := proc(n) local j, a, w; a := array(0..n); a[0] := 1;
for w from 1 to n do a[w]:=a[w-1]-(-1)^w*add(a[j]*a[w-j-1], j=1..w-1) od; convert(a, list)end: A097331_list(48); -Peter Luschny, May 19 2011
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CROSSREFS
| Sequence in context: A105523 A126120 A090192 * A094032 A117780 A155759
Adjacent sequences: A097328 A097329 A097330 * A097332 A097333 A097334
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Aug 05 2004
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