login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A035087 Number of labeled rooted polygonal cacti (Husimi graphs) with n nodes. 3
1, 0, 3, 12, 135, 1440, 20895, 342720, 6585705, 142430400, 3449279295, 92207808000, 2699909867655, 85900402748160, 2951318065570875, 108894519775641600, 4294542443185019025, 180277244225580902400, 8025792422657714379675, 377695544010698833920000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301.

Harary and E. M. Palmer, Graphical Enumeration, p. 71

F. Harary and R. Z. Norman "The Dissimilarity Characteristic of Husimi Trees" Annals of Mathematics, 58 1953, pp. 134-141

F. Harary and G. E. Uhlenbeck "On the Number of Husimi Trees" Proc. Nat. Acad. Sci. USA vol. 39 pp. 315-322 1953

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

FORMULA

E.g.f. satisfies A(x)=x*exp(A(x)^2/(2-2*A(x))).

a(n) ~ (1-s)^2 * sqrt(2/(6-11*s+4*s^2)) * n^(n-1) / (s * exp(1 - s^2/(2*(1-s))))^n, where s = 0.5391888728108891165... is the root of the equation 2-4*s+s^3=0. - Vaclav Kotesovec, Jan 08 2014

MAPLE

A:= proc(n) option remember; if n<=1 then x else convert(series(x* exp(A(n-1)^2/ (2-2*A(n-1))), x=0, n+1), polynom) fi end: a:= n-> coeff(A(n), x, n)*n!: seq(a(n), n=1..30); # Alois P. Heinz, Aug 22 2008

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[E^(x^2/(2*(x-1)))*x, {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)

CROSSREFS

Cf. A035082-A035088.

Sequence in context: A152544 A280115 A264149 * A056426 A056417 A322227

Adjacent sequences:  A035084 A035085 A035086 * A035088 A035089 A035090

KEYWORD

nonn,eigen

AUTHOR

Christian G. Bower, Nov 15 1998

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)