%I M2754 N1107 #27 Aug 30 2018 18:56:58

%S 0,1,1,3,8,26,84,297,1066,3976,15093,58426,229189,910127,3649165,

%T 14756491,60103220,246357081,1015406251,4205873378,17497745509,

%U 73084575666,306352303774,1288328048865,5433980577776,22982025183983

%N Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Christian G. Bower, <a href="/A000237/b000237.txt">Table of n, a(n) for n=0..500</a>

%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>

%H G. W. Ford and G. E. Uhlenbeck, <a href="http://www.jstor.org/stable/89494">Combinatorial problems in the theory of graphs III</a>, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</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 Shifts left under transform T where Ta = EULER(BIK(a)). [See Transforms links.] - _Christian G. Bower_, Nov 15 1998

%o (PARI)

%o BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}

%o EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}

%o seq(n)={my(v=[0]); for(n=1, n, v=concat([0,1], EulerT(Vec(BIK(Ser(v))-1)))); v} \\ _Andrew Howroyd_, Aug 30 2018

%Y Cf. A000083, A000314, A035082, A035349-A035357.

%K nonn,eigen,nice,easy

%O 0,4

%A _N. J. A. Sloane_

%E More terms from _Christian G. Bower_, Nov 15 1998