A323877 Number of labeled graphs on n nodes with four connected components.

0, 0, 0, 1, 10, 125, 2275, 64673, 3102204, 272277040, 46202044900, 15442093276764, 10171924771814520, 13188852179018387144, 33674263441006260931040, 169522275849148918884400912, 1685048703908907788901122512512, 33116110237646373502366665503208064, 1288337109916947580133035603563656989952, 99320901948403913391024993536094346775110656

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, A323875, A323876.

Formula

a(n) = A143543(n+1, 4) for n >= 1 and a(0) = 0.

E.g.f.: log(Sum_{q>=0} 2^binomial(q, 2)*z^q/q!)^4/4!.