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%I #11 Jul 24 2022 10:41:21
%S 1,2,5,14,40,116,344,1040,3188,9880,30912,97520,309856,990656,3184672,
%T 10287808,33379072,108724864,355405568,1165521408,3833497408,
%U 12642775424,41799227392,138512751360,459973953024,1530498526208
%N 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.
%F a(n) = A126219(n,0), i.e., row 0 of triangle A126219.
%F G.f.: (1 - 2z - 4z^3 - sqrt(1 - 8z^3 + 4z^2 - 4z))/(8z^4).
%F 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
%p 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);
%Y Cf. A126219.
%K nonn
%O 0,2
%A _Emeric Deutsch_, Dec 25 2006
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