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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

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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