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A035086 Number of increasing rooted polygonal cacti (Husimi graphs) with n nodes. 3
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
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
Sequence in context: A332621 A091346 A305550 * A215852 A105797 A278189
KEYWORD
nonn,eigen
AUTHOR
Christian G. Bower, Nov 15 1998
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)