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 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 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

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)