cp's OEIS Frontend

A339289 Number of essentially parallel oriented series-parallel networks with n elements and without multiple unit elements in parallel.

%I A339289 #7 Dec 08 2020 02:27:12
%S A339289 1,0,1,2,5,14,39,117,353,1099,3458,11066,35738,116622,383448,1269869,
%T A339289 4230557,14170956,47693457,161207066,546987882,1862464911,6361729689,
%U A339289 21793247587,74855427331,257743707769,889477338903,3076038022778,10658447368514,36998473045302
%N A339289 Number of essentially parallel oriented series-parallel networks with n elements and without multiple unit elements in parallel.
%C A339289 See A339290 for additional details.
%F A339289 G.f.: B(x)/(1 + B(x)) where B(x) is the g.f. of A339290.
%e A339289 In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
%e A339289 a(1) = 1: (o).
%e A339289 a(3) = 1: (o|oo).
%e A339289 a(4) = 2: (o|ooo), (oo|oo).
%e A339289 a(5) = 5: (o|oooo), (o|o(o|oo)), (o|(o|oo)o), (oo|ooo), (o|oo|oo).
%o A339289 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A339289 seq(n, Z=x)={my(p=Z+O(x^2)); for(n=2, n, p = Z + (1 + Z)*x*Ser(EulerT( Vec(p^2/(1+p), -n) ))); Vec(1-1/(1+p))}
%Y A339289 Cf. A339155, A339288, A339290, A339292 (achiral), A339295 (unoriented).
%K A339289 nonn
%O A339289 1,4
%A A339289 _Andrew Howroyd_, Dec 07 2020