A323876 Number of labeled graphs on n nodes with three connected components.
0, 0, 1, 6, 55, 825, 20818, 925036, 76321756, 12143833740, 3786364993664, 2323363153263768, 2810644049356050752, 6714880790313869814368, 31734660624638397560681792, 297106568651256947892439231872, 5516820501457062391874183605225216, 203371936690880564729559424288326233856, 14896201998273652941883043518617399703696384
Offset: 1
Keywords
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.
Formula
a(n) = A143543(n+1, 3) for n >= 1 and a(0) = 0.
E.g.f.: log(Sum_{q>=0} 2^binomial(q, 2)*z^q/q!)^3/3!.