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Search: id:A024492
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| A024492 |
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Catalan numbers with odd index: a(n) = binomial(4*n+2,2*n+1)/(2*n+2). |
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+0
4
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| 1, 5, 42, 429, 4862, 58786, 742900, 9694845, 129644790, 1767263190, 24466267020, 343059613650, 4861946401452, 69533550916004, 1002242216651368, 14544636039226909, 212336130412243110, 3116285494907301262
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Cf. A048990 (Catalan numbers with even index), A024491, A000108.
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FORMULA
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G.f.: A(x) = 1/2*x^-1*(1-sqrt(1/2*(1+sqrt(1-16*x)))).
a(n)=4^n*binomial(2n+1/2, n)/(n+1); - Paul Barry (pbarry(AT)wit.ie), May 10 2005
a(n)=C(4n+1,2n+1)/(n+1); - Paul Barry (pbarry(AT)wit.ie), Nov 09 2006
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EXAMPLE
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sqrt(1/2*(1+sqrt(1-x))) = 1 - 1/8*x - 5/128*x^2 - 21/1024*x^3 - ...
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MAPLE
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with(combstruct):bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, unlabeled], size=2*n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 05 2007
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PROGRAM
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(Mupad) combinat::catalan(2*n+1)$ n = 0..24 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008
(Mupad) combinat::dyckWords::count(2*n+1)$ n = 0..24 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 02 2008
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CROSSREFS
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Sequence in context: A062021 A082145 A126765 this_sequence A005789 A151334 A102693
Adjacent sequences: A024489 A024490 A024491 this_sequence A024493 A024494 A024495
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
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More terms from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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