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%I #29 Jul 21 2021 16:01:12
%S 1,1,2,8,41,253,1858,15796,152219,1638323,19467494,252998224,
%T 3568259503,54263159347,884834059454,15397757661092,284767413357977,
%U 5576696746139689,115269732256964626,2507575465491619672,57262481225957071721,1369461739453440893261
%N Number of graphs on n labeled nodes with degree at most 2.
%C These are thunderstorm graphs. Their connected components are a single cycle (clouds), a path (lightning bolts) or an isolated vertex (raindrops). - _Geoffrey Critzer_, May 11 2011
%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.4.
%H Alois P. Heinz, <a href="/A136281/b136281.txt">Table of n, a(n) for n = 0..445</a> (terms n=1..200 from Vincenzo Librandi)
%H Samuele Giraudo, <a href="https://arxiv.org/abs/1709.08416">Combalgebraic structures on decorated cliques</a>, Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire, 78B.15, 2017, p. 8, arXiv:1709.08416 [math.CO], 2017.
%F Binomial transform of A000986. E.g.f.: (1-x)^(-1/2)*exp(-x^2/4 + x/((2*(1-x)))). - _Vladeta Jovovic_, May 20 2008
%F a(n) = (2*n-1)*a(n-1) - (n-1)^2*a(n-2) + (n-2)*(n-1)*a(n-3) - (n-3)*(n-2)*(n-1)/2*a(n-4). - _Vaclav Kotesovec_, Aug 10 2013
%F a(n) ~ n^n*exp(sqrt(2*n)-1/2-n)/sqrt(2) * (1+19/(24*sqrt(2*n))). - _Vaclav Kotesovec_, Aug 10 2013
%t f = (Log[1/(1-x)]+1/(1-x) -x^2/2 - 1)/2;
%t Range[0,25]! CoefficientList[Series[Exp[f],{x,0,25}],x] (* _Geoffrey Critzer_, May 11 2011 *)
%Y Cf. A000085 (degree at most 1), A136282-A136286.
%K nonn
%O 0,3
%A _Don Knuth_, Mar 31 2008
%E More terms from _Vladeta Jovovic_, May 20 2008
%E a(0)=1 prepended by _Alois P. Heinz_, Jul 21 2021
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