A323876 -id:A323876 - cp's OEIS frontend

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

Marko Riedel, Feb 05 2019

nonn

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

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

Cf. A143543, A323876, A323877.

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

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

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

Original entry on oeis.org

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

Offset: 1

Marko Riedel, Feb 05 2019

nonn

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

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

Cf. A143543, A323875, A323876.

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!.

cp's OEIS Frontend

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

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