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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Column 0 of A114626.
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FORMULA
| 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
| a(1)=2 because we have UUUDUDDD and UUUUDDDD, where U=(1,1), D=(1,-1).
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MAPLE
| 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
| Cf. A114626.
Sequence in context: A052975 A035929 A071646 * A148464 A148465 A148466
Adjacent sequences: A114624 A114625 A114626 * A114628 A114629 A114630
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 18 2005
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