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A127539
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Number of ordered trees with n edges having no odd-length branches starting at the root.
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2
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1, 0, 1, 0, 3, 3, 16, 37, 134, 411, 1411, 4747, 16500, 57671, 204380, 730032, 2629637, 9535268, 34787215, 127585608, 470162614, 1739952061, 6463845941, 24096378885, 90112499714, 337965831635, 1270901550454, 4790836498608, 18100497143361
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OFFSET
| 0,5
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COMMENTS
| a(n)=A127538(n,0).
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FORMULA
| G.f.=(1+z)*C/(C+z), where C =[1-sqrt(1-4z)]/(2z) is the Catalan function.
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EXAMPLE
| a(3)=0 because all five ordered trees with 3 edges have at least one odd-length branch starting at the root.
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MAPLE
| C:=(1-sqrt(1-4*z))/2/z: G:=(1+z)*C/(C+z): Gser:=series(G, z=0, 35): seq(coeff(Gser, z, n), n=0..31);
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CROSSREFS
| Cf. A127538, A000958.
Sequence in context: A089403 A111674 A048234 * A014783 A090524 A095106
Adjacent sequences: A127536 A127537 A127538 * A127540 A127541 A127542
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 01 2007
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