This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339288 #10 Dec 08 2020 15:23:26
%S A339288 0,1,1,3,8,22,64,189,577,1788,5642,18016,58213,189792,623913,2065219,
%T A339288 6878429,23032917,77500237,261892491,888439320,3024510467,10329241959,
%U A339288 35379140285,121502993735,418306868672,1443409882944,4991122973019,17292424070839,60021140494647,208684858267921
%N A339288 Number of essentially series oriented series-parallel networks with n elements and without multiple unit elements in parallel.
%C A339288 See A339290 for additional details.
%F A339288 G.f.: P(x)^2/(1 - P(x)) where P(x) is the g.f. of A339289.
%F A339288 G.f.: B(x)^2/(1 + B(x)) where B(x) is the g.f. of A339290.
%e A339288 In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
%e A339288 a(2) = 1: (oo).
%e A339288 a(3) = 1: (ooo).
%e A339288 a(4) = 3: (oooo), (o(o|oo)), ((o|oo)o).
%e A339288 a(5) = 8: (ooooo), (oo(o|oo)), (o(o|oo)o), ((o|oo)oo), (o(o|ooo)), (o(oo|oo)), ((o|ooo)o), ((oo|oo)o).
%o A339288 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A339288 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(p - p/(1+p), -n)}
%Y A339288 Cf. A339154, A339289, A339290, A339291 (achiral), A339294 (unoriented).
%K A339288 nonn
%O A339288 1,4
%A A339288 _Andrew Howroyd_, Dec 07 2020