A126220 Number of binary trees (i.e., rooted trees where each vertex has either 0, 1, or 2 children; and, when only one child is present, it is either a right child or a left child) with n edges and no adjacent vertices of outdegree 2.

1, 2, 5, 14, 40, 116, 344, 1040, 3188, 9880, 30912, 97520, 309856, 990656, 3184672, 10287808, 33379072, 108724864, 355405568, 1165521408, 3833497408, 12642775424, 41799227392, 138512751360, 459973953024, 1530498526208

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) = A126219(n,0), i.e., row 0 of triangle A126219.

G.f.: (1 - 2z - 4z^3 - sqrt(1 - 8z^3 + 4z^2 - 4z))/(8z^4).

D-finite with recurrence (n+4)*a(n) +2*(-2*n-5)*a(n-1) +4*(n+1)*a(n-2) +4*(-2*n+1)*a(n-3)=0. - R. J. Mathar, Jun 17 2016

Maple

g:=(1-4*z^3-2*z-sqrt(1-8*z^3+4*z^2-4*z))/8/z^4: gser:=series(g, z=0, 35): seq(coeff(gser, z, n), n=0..30);

Crossrefs

Cf. A126219.

Sequence in context: A036908 A293346 A273900 * A136304 A190254 A075496

Adjacent sequences: A126217 A126218 A126219 * A126221 A126222 A126223

Keyword

nonn

Author

Emeric Deutsch, Dec 25 2006

Status

approved