cp's OEIS Frontend

A000237 Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.

%I A000237 M2754 N1107 #27 Aug 30 2018 18:56:58
%S A000237 0,1,1,3,8,26,84,297,1066,3976,15093,58426,229189,910127,3649165,
%T A000237 14756491,60103220,246357081,1015406251,4205873378,17497745509,
%U A000237 73084575666,306352303774,1288328048865,5433980577776,22982025183983
%N A000237 Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.
%D A000237 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000237 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000237 Christian G. Bower, <a href="/A000237/b000237.txt">Table of n, a(n) for n=0..500</a>
%H A000237 C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H A000237 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 A000237 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A000237 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%H A000237 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%H A000237 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A000237 Shifts left under transform T where Ta = EULER(BIK(a)). [See Transforms links.] - _Christian G. Bower_, Nov 15 1998
%o A000237 (PARI)
%o A000237 BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}
%o A000237 EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A000237 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 A000237 Cf. A000083, A000314, A035082, A035349-A035357.
%K A000237 nonn,eigen,nice,easy
%O A000237 0,4
%A A000237 _N. J. A. Sloane_
%E A000237 More terms from _Christian G. Bower_, Nov 15 1998