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A127539 Number of ordered trees with n edges having no odd-length branches starting at the root. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

a(n)=A127538(n,0).

LINKS

Table of n, a(n) for n=0..28.

FORMULA

G.f.=(1+z)*C/(C+z), where C =[1-sqrt(1-4z)]/(2z) is the Catalan function.

EXAMPLE

a(3)=0 because all five ordered trees with 3 edges have at least one odd-length branch starting at the root.

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);

CROSSREFS

Cf. A127538, A000958.

Sequence in context: A222847 A278309 A048234 * A278627 A231908 A226610

Adjacent sequences:  A127536 A127537 A127538 * A127540 A127541 A127542

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Mar 01 2007

STATUS

approved

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Last modified October 17 22:21 EDT 2019. Contains 328134 sequences. (Running on oeis4.)