

A127539


Number of ordered trees with n edges having no oddlength 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
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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 =[1sqrt(14z)]/(2z) is the Catalan function.


EXAMPLE

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


MAPLE

C:=(1sqrt(14*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: A278309 A048234 A068415 * A342837 A278627 A231908
Adjacent sequences: A127536 A127537 A127538 * A127540 A127541 A127542


KEYWORD

nonn


AUTHOR

Emeric Deutsch, Mar 01 2007


STATUS

approved



