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Search: id:A002067
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| A002067 |
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a(n) = Sum_{k=0..n-1} binomial(2*n,2*k)*a(k)*a(n-k-1).
(Formerly M4458 N1889)
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+0
7
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| 1, 1, 7, 127, 4369, 243649, 20036983, 2280356863, 343141433761, 65967241200001, 15773461423793767, 4591227123230945407, 1598351733247609852849, 655782249799531714375489, 313160404864973852338669783, 172201668512657346455126457343, 108026349476762041127839800617281
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Also number of increasing rooted triangular cacti of 2n+1 nodes. (In an increasing rooted graph, nodes are numbered and numbers increase as you move away from root.)
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
Cf. Chapter 5 of F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..50
Wikipedia, Error Function
Index entries for sequences related to cacti
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FORMULA
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We have a(n)=b(2n+1), where e.g.f. of b satisfies B'(x)=exp(B(x)^2/2).
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MAPLE
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a:=proc(n) option remember; if n <= 0 then RETURN(1); else RETURN( add( binomial(2*n, 2*k)*a(k)*a(n-k-1), k=0..n-1 ) ); fi; end;
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CROSSREFS
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The sequence of fractions A092676/A132467 is closely related.
Periods: A122149, A122159.
Adjacent sequences: A002064 A002065 A002066 this_sequence A002068 A002069 A002070
Sequence in context: A025166 A139291 A092676 this_sequence A138523 A034670 A020516
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KEYWORD
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nonn,eigen,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Alternate description, formula and comment from Christian G. Bower (bowerc(AT)usa.net).
New definition and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 22 2005
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