This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A035086 Number of increasing rooted polygonal cacti (Husimi graphs) with n nodes. 2
 1, 0, 1, 3, 19, 135, 1204, 12537, 150556, 2043930, 30969211, 517973148, 9478800604, 188381470095, 4040440921699, 93020386382742, 2287969523647171, 59877222907995675, 1661259526266784171, 48705364034046758493, 1504614657169716311674, 48848750173492332588525 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Nodes are numbered and the numbers increase as you move away from the root to any point on the same polygon. REFERENCES F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 301 and Chapter 5. F. Harary and E. M. Palmer, Graphical Enumeration, p. 71. LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 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. FORMULA E.g.f. satisfies A'(x) = exp(A(x)^2/(2-2*A(x))). MAPLE A:= proc(n) option remember; if n<=1 then x else convert(series(Int(exp(A(n-1)^2/ (2-2*A(n-1))), x), x=0, n+1), polynom) fi end; a:= n-> coeff(A(n), x, n)*n!: seq(a(n), n=1..22); # Alois P. Heinz, Aug 22 2008 MATHEMATICA max = 22; sy = Series[Integrate[E^(-(y^2/(2-2*y))), y], {y, 0, max}]; sx = Normal[ InverseSeries[sy, x]]; a[n_] := Coefficient[sx, x, n]*n!; Table[a[n], {n, 1, max }] (* Jean-François Alcover, Feb 24 2015 *) CROSSREFS Cf. A035082-A035088. Sequence in context: A074567 A091346 A305550 * A215852 A105797 A278189 Adjacent sequences:  A035083 A035084 A035085 * A035087 A035088 A035089 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.

Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)