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

0, 1, 1, 3, 8, 26, 84, 297, 1066, 3976, 15093, 58426, 229189, 910127, 3649165, 14756491, 60103220, 246357081, 1015406251, 4205873378, 17497745509, 73084575666, 306352303774, 1288328048865, 5433980577776, 22982025183983

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• eigen
• nice
• easy

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Christian G. Bower, Table of n, a(n) for n=0..500
• C. G. Bower, Transforms (2)
• G. W. Ford and G. E. Uhlenbeck, Combinatorial problems in the theory of graphs III, Proc. Nat. Acad. Sci. USA, 42 (1956), 529-535.
• N. J. A. Sloane, Transforms
• Index entries for sequences related to cacti
• Index entries for sequences related to rooted trees
• Index entries for sequences related to trees

Crossrefs

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

Programs

PARI

BIK(p)={(1/(1-p) + (1+p)/subst(1-p, x, x^2))/2}
EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
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

Formula

Shifts left under transform T where Ta = EULER(BIK(a)). [See Transforms links.] - Christian G. Bower, Nov 15 1998

Extensions

More terms from Christian G. Bower, Nov 15 1998