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

0,5

References

J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence R_n).

Links

Table of n, a(n) for n=0..20.

Index entries for sequences mentioned in Moon (1987)

S. R. Finch, Series-parallel networks

S. R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author]

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

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 *)

Crossrefs

Cf. A058379, A058381.

Sequence in context: A268777 A109727 A041320 * A129746 A067863 A257809

Adjacent sequences: A058377 A058378 A058379 * A058381 A058382 A058383

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Dec 19 2000

Status

approved