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A342988 Number of tree-rooted planar maps with n edges and no isthmuses.

%I A342988 #9 Apr 03 2021 22:52:09
%S A342988 1,1,4,23,162,1292,11214,103497,1000810,10039100,103725188,1098151276,
%T A342988 11866435816,130477138014,1456320910090,16468167354971,
%U A342988 188369396046810,2176619115192140,25379588118629856,298341351434460488,3532848638781046852,42113699799069958732
%N A342988 Number of tree-rooted planar maps with n edges and no isthmuses.
%H A342988 Andrew Howroyd, <a href="/A342988/b342988.txt">Table of n, a(n) for n = 0..500</a>
%F A342988 G.f.: A(x) satisfies A(x) = G(x*A(x)^2) where G(x) + x is the g.f. of A004304.
%o A342988 (PARI) \\ here J(n) gives A004304 as g.f.
%o A342988 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 A342988 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 A342988 Row sums of A342987.
%Y A342988 Cf. A004304, A342986.
%K A342988 nonn
%O A342988 0,3
%A A342988 _Andrew Howroyd_, Apr 03 2021