A000237 Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges. (Formerly M2754 N1107)

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

0,4

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

Formula

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

Prog

(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

Crossrefs

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

Sequence in context: A148803 A148804 A148805 * A148806 A148807 A148808

Adjacent sequences: A000234 A000235 A000236 * A000238 A000239 A000240

Keyword

nonn,eigen,nice,easy

Author

N. J. A. Sloane

Extensions

More terms from Christian G. Bower, Nov 15 1998

Status

approved