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Search: id:A114627
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| A114627 |
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Number of hill-free Dyck paths of semilength n+3 and having no peaks at level 2 (a Dyck path is said to be hill-free if it has no peaks at level 1). |
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+0
2
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| 1, 2, 6, 19, 61, 202, 683, 2348, 8184, 28855, 102731, 368813, 1333684, 4853436, 17761181, 65320691, 241300829, 894958140, 3331323651, 12441078958, 46601721324, 175040968111, 659136721385, 2487852579751, 9410480922018
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Column 0 of A114626.
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FORMULA
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G.f.=(C-1)/[z(1+z+z^2-z(1+z)C], where C=[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
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a(1)=2 because we have UUUDUDDD and UUUUDDDD, where U=(1,1), D=(1,-1).
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MAPLE
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C:=(1-sqrt(1-4*z))/2/z: G:=(C-1)/z/(1+z+z^2-z*(1+z)*C): Gser:=series(G, z=0, 32): 1, seq(coeff(Gser, z^n), n=1..28);
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CROSSREFS
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Cf. A114626.
Sequence in context: A052975 A035929 A071646 this_sequence A094817 A033565 A094831
Adjacent sequences: A114624 A114625 A114626 this_sequence A114628 A114629 A114630
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 18 2005
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