A058380 - OEIS

%I #21 May 30 2026 16:40:07

%S 0,0,1,1,13,66,796,8338,122326,1893748,34717076,695343144,15560613872,

%T 379211091416,10070672083928,288420300817184,8877044175277216,

%U 291944826030636000,10221726849956763136,379528960298122277536,14896869800297864928736

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

%H Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/">Series-parallel networks</a>

%H Steven R. Finch, <a href="/A000084/a000084_2.pdf">Series-parallel networks</a>, July 7, 2003. [Cached copy, with permission of the author]

%H John W. Moon, <a href="https://doi.org/10.1016/S0304-0208(08)73057-3">Some enumerative results on series-parallel networks</a>, Annals Discrete Math., 33 (1987), 199-226 (the sequence R_n).

%H <a href="/index/Mo#Moon87">Index entries for sequences mentioned in Moon (1987)</a>

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

%F E.g.f.: -1/2 - log(1+x)/2 - LambertW(-exp(-1/2)*sqrt(1+x)/2). - _Vaclav Kotesovec_, Mar 11 2014

%F a(n) ~ n^(n-1) / (2*sqrt(2)*(4-exp(1))^(n-1/2)). - _Vaclav Kotesovec_, Mar 11 2014

%t 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 *)

%Y Cf. A058379, A058381.

%K nonn,nice,easy

%O 0,5

%A _N. J. A. Sloane_, Dec 19 2000