A378078 - OEIS

%I #8 Nov 21 2024 22:26:26

%S 1,1,3,12,50,219,987,4552,21366,101730,490094,2384520,11699844,

%T 57825103,287611755,1438536144,7230782414,36506547918,185047345050,

%U 941359362760,4804468999932,24593960996814,126239765780606,649610643221616,3350542070046300,17318377059738820

%N Number of noncrossing trees with n edges and all nodes having degree at most 3.

%H Andrew Howroyd, <a href="/A378078/b378078.txt">Table of n, a(n) for n = 0..500</a>

%F G.f.: (1 + g(x) + g(x)^2 + g(x)^3) where g(x)/x is the g.f. of A122871.

%e a(4) = A001764(4) - 5 where the 5 trees excluded are those with one node connected to the other four.

%o (PARI) seq(n)={my(g=serreverse(x/(1+2*x+3*x^2) + O(x*x^n))); Vec(1 + g + g^2 + g^3)}

%Y Cf. A001764, A122871, A378079.

%K nonn

%O 0,3

%A _Andrew Howroyd_, Nov 21 2024