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%I #9 Apr 03 2021 22:52:09
%S 1,1,4,23,162,1292,11214,103497,1000810,10039100,103725188,1098151276,
%T 11866435816,130477138014,1456320910090,16468167354971,
%U 188369396046810,2176619115192140,25379588118629856,298341351434460488,3532848638781046852,42113699799069958732
%N Number of tree-rooted planar maps with n edges and no isthmuses.
%H Andrew Howroyd, <a href="/A342988/b342988.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) + 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)-x, p=O(1)); while(serprec(p, x)<=n, p = subst(g, x, x*p^2)); Vec(p)}
%Y Row sums of A342987.
%Y Cf. A004304, A342986.
%K nonn
%O 0,3
%A _Andrew Howroyd_, Apr 03 2021
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