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%I #28 Jun 22 2018 23:14:28
%S 1,1,3,16,122,1203,14518,207061,3406083,63465271,1320938774,
%T 30371545338,764447981599,20904838435264,617151430504113,
%U 19561785238965715,662583041367287249,23882958184429006800,912777131398463190802,36868849734952579404745
%N Number of increasing rooted polygonal cacti with bridges (mixed Husimi trees) with n nodes.
%C Limit n->infinity (a(n)/n!)^(1/n) = 2.168573... - _Vaclav Kotesovec_, Feb 28 2014
%H Alois P. Heinz, <a href="/A035352/b035352.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F E.g.f. satisfies A'(x) = exp((2*A(x)-A(x)^2)/(2-2*A(x))).
%p Ap:= proc(n) option remember; local A, f; if n<=0 then f:=1 else A:= Int(Ap(n-1),x); f:= exp((2*A -A^2)/ (2-2*A)) fi; convert(series(f, x, n+1), polynom) end: a:= n-> coeff(series(Ap(n-1), x=0,n), x,n-1)*(n-1)!: seq(a(n), n=1..30); # _Alois P. Heinz_, Aug 20 2008
%t Ap[n_] := Ap[n] = Module[{A, f}, If[n <= 0, f=1, A = Integrate[Ap[n-1], x]; f = Exp[(2*A-A^2)/(2-2*A)]]; Series[f, {x, 0, n+1}] // Normal]; a[n_] := SeriesCoefficient[Ap[n-1], {x, 0, n-1}]*(n-1)!; Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, Feb 24 2016, after _Alois P. Heinz_ *)
%Y Cf. A000083, A000237, A000314, A035082, A035349-A035357.
%K nonn,eigen
%O 1,3
%A _Christian G. Bower_, Nov 15 1998
%E a(18) corrected by _Alois P. Heinz_, Aug 20 2008
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