A058380 Essentially series series-parallel networks with n labeled edges, multiple edges not allowed.

0, 0, 1, 1, 13, 66, 796, 8338, 122326, 1893748, 34717076, 695343144, 15560613872, 379211091416, 10070672083928, 288420300817184, 8877044175277216, 291944826030636000, 10221726849956763136, 379528960298122277536, 14896869800297864928736

Offset: 0

Author

N. J. A. Sloane, Dec 19 2000

Keywords

• nonn
• nice
• easy

Links

• Steven R. Finch, Series-parallel networks
• Steven R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]
• John W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence R_n).
• Index entries for sequences mentioned in Moon (1987)

Crossrefs

Cf. A058379, A058381.

Programs

Mathematica

CoefficientList[Series[-1/2 - Log[1+x]/2 - LambertW[-E^(-1/2)*Sqrt[1+x]/2], {x, 0, 15}], x]* Range[0, 15]! (* Vaclav Kotesovec, Mar 11 2014 *)

Formula

E.g.f. satisfies A(x) = A058379(x) - log(1+x).

E.g.f.: -1/2 - log(1+x)/2 - LambertW(-exp(-1/2)*sqrt(1+x)/2). - Vaclav Kotesovec, Mar 11 2014

a(n) ~ n^(n-1) / (2*sqrt(2)*(4-exp(1))^(n-1/2)). - Vaclav Kotesovec, Mar 11 2014