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 A339155 Number of essentially parallel oriented series-parallel networks with n elements and without unit elements in parallel. 3
 1, 0, 0, 1, 1, 3, 5, 13, 29, 70, 165, 409, 1001, 2505, 6278, 15904, 40447, 103567, 266229, 687668, 1782573, 4637731, 12103112, 31679212, 83135973, 218713492, 576683119, 1523740365, 4033915677, 10698680606, 28422818782, 75629586540, 201539697208, 537818080714 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS A series configuration is an ordered concatenation of two or more parallel configurations and a parallel configuration is the unit element or a multiset of two or more series configurations. a(n) is the number of parallel configurations with n unit elements. LINKS FORMULA G.f.: B(x)/(1 + B(x)) where B(x) is the g.f. of A339156. EXAMPLE In the following examples, elements in series are juxtaposed and elements in parallel are separated by '|'. The unit element is denoted by 'o'. a(1) = 1: (o). a(4) = 1: (oo|oo). a(5) = 1: (oo|ooo). a(6) = 3: (oo|oooo), (ooo|ooo), (oo|oo|oo). a(7) = 4: (oo|ooooo), (oo|o(oo|oo)), (oo|(oo|oo)o), (ooo|oooo), (oo|oo|ooo). PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(p=x+O(x^2)); for(n=2, n, p=x+x*Ser(EulerT(Vec(p^2/(1+p), -n)))); Vec(1 - 1/(1+p))} CROSSREFS Cf. A003430, A339152, A339154, A339156. Sequence in context: A290113 A238216 A067932 * A168314 A335562 A106666 Adjacent sequences:  A339152 A339153 A339154 * A339156 A339157 A339158 KEYWORD nonn AUTHOR Andrew Howroyd, Nov 26 2020 STATUS approved

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)