cp's OEIS Frontend

A339153 Number of nonequivalent series-parallel networks with n elements and without unit elements in parallel.

%I A339153 #5 Nov 26 2020 21:59:28
%S A339153 1,1,1,2,3,6,10,20,37,74,144,295,594,1229,2540,5324,11177,23684,50326,
%T A339153 107593,230743,497008,1073667,2327213,5057433,11020414,24068945,
%U A339153 52685541,115555511,253933732,558993308,1232569467,2721958234,6019784562,13331192017,29560633824
%N A339153 Number of nonequivalent series-parallel networks with n elements and without unit elements in parallel.
%C A339153 Equivalence is up to rearrangement of the order of elements in both series and parallel configurations.
%C A339153 A series configuration is a multiset of two or more parallel configurations and a parallel configuration is a multiset of two or more series configurations. The unit element is considered to be a parallel configuration.
%F A339153 a(n) = A339151(n) + A339152(n).
%F A339153 Euler transform of A339152.
%F A339153 Euler transform of A339151 gives this sequence with a(1) = 0.
%e A339153 In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'.
%e A339153 a(1) = 1: (o).
%e A339153 a(2) = 1: (oo).
%e A339153 a(3) = 1: (ooo).
%e A339153 a(4) = 2: (oooo), (oo|oo).
%e A339153 a(5) = 3: (ooooo), (o(oo|oo)), (oo|ooo).
%e A339153 a(6) = 6: (oooooo), (oo(oo|oo)), (o(oo|ooo)), (oo|oooo), (ooo|ooo), (oo|oo|oo).
%o A339153 (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
%o A339153 seq(n)={my(S=vector(n), P=vector(n)); P[1]=1; for(n=2, #S, my(t=EulerT(S[1..n])[n]); S[n]=EulerT(P[1..n])[n]; P[n]=t); S+P}
%Y A339153 Cf. A000669, A339151, A339152.
%K A339153 nonn
%O A339153 1,4
%A A339153 _Andrew Howroyd_, Nov 26 2020