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 A091485 Number of labeled 2,3 cacti (triangular cacti with bridges). 1
 1, 1, 4, 28, 290, 3996, 68992, 1434112, 34895772, 973450000, 30636233936, 1074020373504, 41510792057176, 1753764940408768, 80412829785000000, 3977094146761424896, 211058327532167398928, 11963018212810373415168, 721321146876339731628352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS As Alois P. Heinz has pointed out, the e.g.f in the Example section does not match the offset. However, the identity a(n) = A091481(n)/n holds with the present offset of 1. - N. J. A. Sloane, Jun 23 2017 REFERENCES F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.84). LINKS Maryam Bahrani and Jérémie Lumbroso, Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition, arXiv:1608.01465 [math.CO], 2016. FORMULA a(n) = A091481(n)/n. From Paul D. Hanna, Jun 01 2012: (Start) E.g.f.: (1/x)*Series_Reversion( x/exp(x+x^2/2) ). E.g.f. satisfies: A(x) = exp( x*A(x) + x^2*A(x)^2/2 ). E.g.f. satisfies: A( x/exp(x+x^2/2) ) = exp(x+x^2/2). (End) EXAMPLE E.g.f.: A(x) = 1 + x + 4*x^2/2! + 28*x^3/3! + 290*x^4/4! + 3996*x^5/5! +... MATHEMATICA CoefficientList[1/x InverseSeries[x/Exp[x+x^2/2]+O[x]^20], x] Range[0, 18]! (* Jean-François Alcover, Aug 06 2018 *) CROSSREFS Cf. A091487, A000085. Sequence in context: A201595 A076729 A078634 * A201354 A112938 A307083 Adjacent sequences:  A091482 A091483 A091484 * A091486 A091487 A091488 KEYWORD nonn AUTHOR Christian G. Bower, Jan 14 2004 STATUS approved

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Last modified August 1 03:52 EDT 2021. Contains 346384 sequences. (Running on oeis4.)