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

1,3

References

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

Links

Table of n, a(n) for n=1..18.

Marko Riedel et al., Proof of recurrence relation.

Marko Riedel, Maple implementation of memoized recurrence.

Formula

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

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

Crossrefs

Cf. A143543, A323876, A323877.

Sequence in context: A198046 A295812 A228229 * A001929 A349962 A230316

Adjacent sequences: A323872 A323873 A323874 * A323876 A323877 A323878

Keyword

nonn

Author

Marko Riedel, Feb 05 2019

Status

approved