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%I #10 Apr 03 2021 22:51:53
%S 1,0,2,6,44,280,2100,16310,133652,1132992,9895672,88520520,808057712,
%T 7504219008,70730676392,675328163542,6521495669380,63612394972608,
%U 626076210568200,6211621325369992,62077602307372720,624488579671582880,6320044589443116720,64313288809475362888
%N Number of tree-rooted loopless planar maps with n edges and no isthmuses.
%H Andrew Howroyd, <a href="/A342986/b342986.txt">Table of n, a(n) for n = 0..500</a>
%F G.f.: A(x) satisfies A(x) = G(x*A(x)^2) where G(x) + 2*x is the g.f. of A004304.
%o (PARI) \\ here J(n) gives A004304 as g.f.
%o J(n)={my(g=(1-sqrt(1-4*x+O(x^3*x^n)))/(2*x), h=serconvol(g, (g-1)/x));sqrt(x/serreverse(x*h^2))}
%o seq(n)={my(g=J(n)-2*x, p=O(1)); while(serprec(p, x)<=n, p = subst(g, x, x*p^2)); Vec(p)}
%Y Row sums of A342985.
%Y Cf. A004304, A342988.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Apr 03 2021
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