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A323875 Number of labeled graphs on n nodes with two connected components. 3

%I #23 Feb 26 2019 05:02:48

%S 0,1,3,19,230,5098,207536,15891372,2343580752,675458276144,

%T 383306076989440,430041136692146912,956431386434331323776,

%U 4224539434553753578497024,37106501188130085159785113344,648740172906485727983524271405824,22591360806791558877526051411343415296,1567817808096346724727108606144936617617408

%N Number of labeled graphs on n nodes with two connected components.

%D F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, 1973, section 1.2.

%H Marko Riedel et al., <a href="https://math.stackexchange.com/questions/3094635/">Proof of recurrence relation.</a>

%H Marko Riedel, <a href="/A323875/a323875.maple.txt">Maple implementation of memoized recurrence.</a>

%F a(n) = A143543(n, 2).

%F E.g.f.: log(Sum_{q>=0} 2^binomial(q, 2)*z^q/q!)^2/2!.

%Y Cf. A143543, A323876, A323877.

%K nonn

%O 1,3

%A _Marko Riedel_, Feb 05 2019

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)