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
Keywords
Crossrefs
Cf. A126219.
Programs
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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);
Formula
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