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

0, 1, 3, 19, 230, 5098, 207536, 15891372, 2343580752, 675458276144, 383306076989440, 430041136692146912, 956431386434331323776, 4224539434553753578497024, 37106501188130085159785113344, 648740172906485727983524271405824, 22591360806791558877526051411343415296, 1567817808096346724727108606144936617617408

Offset: 1

Author

Marko Riedel, Feb 05 2019

Keywords

• nonn

References

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

Links

• Marko Riedel et al., Proof of recurrence relation.
• Marko Riedel, Maple implementation of memoized recurrence.

Crossrefs

Cf. A143543, A323876, A323877.

Formula

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

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