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%I #10 Aug 30 2018 18:56:22
%S 1,0,0,0,0,1,3,7,21,57,159,435,1217,3400,9633,27413,78733,227489,
%T 661984,1937211,5701733,16865522,50126650,149627241,448448400,
%U 1349060262,4072508115,12333762442,37466367898,114133581762
%N Number of asymmetric 2,3 cacti (triangular cacti with bridges).
%H Andrew Howroyd, <a href="/A091489/b091489.txt">Table of n, a(n) for n = 1..500</a>
%H <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F G.f.: A(x) = B(x)-B(x)^2/2-B(x^2)/2+B(x^3)/3-B(x)^3/3 where B is g.f. of A091488
%o (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
%o b(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(WeighT(Vec(p + (p^2 - subst(p,x,x^2))/2))))); p}
%o seq(n)={my(p=b(n)); Vec(p - p^2/2 - p^3/3 - subst(p, x, x^2)/2 + subst(p, x, x^3)/3)} \\ _Andrew Howroyd_, Aug 30 2018
%Y Cf. A091487, A091488.
%K nonn
%O 1,7
%A _Christian G. Bower_, Jan 14 2004
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