A127539 Number of ordered trees with n edges having no odd-length branches starting at the root.

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

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.

D-finite with recurrence (-n+1)*a(n) +2*(n-3)*a(n-1) +(7*n-25)*a(n-2) +(3*n-17)*a(n-3) +(3*n-7)*a(n-4) +2*(2*n-9)*a(n-5)=0. - R. J. Mathar, Jul 26 2022

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: A278309 A048234 A068415 * A342837 A278627 A231908

Adjacent sequences: A127536 A127537 A127538 * A127540 A127541 A127542

Keyword

nonn

Author

Emeric Deutsch, Mar 01 2007

Status

approved