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A378079 Number of series-reduced noncrossing trees with n edges.

%I A378079 #6 Nov 21 2024 22:26:22
%S A378079 1,1,0,4,5,33,91,408,1485,6195,24838,103752,432796,1834140,7815900,
%T A378079 33591376,145197017,631281591,2757917260,12102728740,53321334381,
%U A378079 235768155073,1045889996047,4653534540816,20761857325000,92862669150004,416316199107096,1870414803490240
%N A378079 Number of series-reduced noncrossing trees with n edges.
%H A378079 Andrew Howroyd, <a href="/A378079/b378079.txt">Table of n, a(n) for n = 0..500</a>
%F A378079 G.f.: 1/(1 - g(x)) - g(x)^2 where g(x) is the g.f. of A030980.
%e A378079 The a(3) = 4 trees are:
%e A378079     o---o    o---o    o   o    o   o
%e A378079     | \        / |    | /        \ |
%e A378079     o   o    o   o    o---o    o---o
%o A378079 (PARI) seq(n)={my(g=serreverse(x/(1/(1-x)^2 - 2*x) + O(x*x^n))); Vec(1/(1 - g) - g^2)}
%Y A378079 Cf. A000014, A001764, A030980, A378078.
%K A378079 nonn
%O A378079 0,4
%A A378079 _Andrew Howroyd_, Nov 21 2024