This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091485 #27 Aug 19 2023 19:04:07
%S A091485 1,1,4,28,290,3996,68992,1434112,34895772,973450000,30636233936,
%T A091485 1074020373504,41510792057176,1753764940408768,80412829785000000,
%U A091485 3977094146761424896,211058327532167398928,11963018212810373415168,721321146876339731628352
%N A091485 Number of labeled 2,3 cacti (triangular cacti with bridges).
%C A091485 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
%D A091485 F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 185 (3.1.84).
%H A091485 Maryam Bahrani and Jérémie Lumbroso, <a href="http://arxiv.org/abs/1608.01465">Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition</a>, arXiv:1608.01465 [math.CO], 2016.
%H A091485 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A091485 a(n) = A091481(n)/n.
%F A091485 From _Paul D. Hanna_, Jun 01 2012: (Start)
%F A091485 E.g.f.: (1/x)*Series_Reversion( x/exp(x+x^2/2) ).
%F A091485 E.g.f. satisfies: A(x) = exp( x*A(x) + x^2*A(x)^2/2 ).
%F A091485 E.g.f. satisfies: A( x/exp(x+x^2/2) ) = exp(x+x^2/2).
%F A091485 (End)
%F A091485 a(n+1) = n! * Sum_{k=0..n} (1/2)^(n-k) * (n+1)^(k-1) * binomial(k,n-k)/k!. - _Seiichi Manyama_, Aug 19 2023
%e A091485 E.g.f.: A(x) = 1 + x + 4*x^2/2! + 28*x^3/3! + 290*x^4/4! + 3996*x^5/5! +...
%t A091485 CoefficientList[1/x InverseSeries[x/Exp[x+x^2/2]+O[x]^20], x] Range[0, 18]! (* _Jean-François Alcover_, Aug 06 2018 *)
%Y A091485 Cf. A091481, A091487, A000085.
%K A091485 nonn
%O A091485 1,3
%A A091485 _Christian G. Bower_, Jan 14 2004