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 A339154 Number of essentially series oriented series-parallel networks with n elements and without unit elements in parallel. 3
 0, 1, 1, 1, 3, 6, 14, 30, 70, 165, 397, 961, 2368, 5875, 14722, 37134, 94312, 240823, 618147, 1593606, 4125218, 10717064, 27934867, 73032798, 191464677, 503218042, 1325678981, 3499913710, 9258627528, 24538328431, 65147600774, 173243773337, 461400769439 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 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 series configurations with n unit elements. LINKS FORMULA G.f.: P(x)^2/(1 - P(x)) where P(x) is the g.f. of A339155. G.f.: B(x)^2/(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(2) = 1: (oo). a(3) = 1: (ooo). a(4) = 1: (oooo). a(5) = 3: (ooooo), (o(oo|oo)), ((oo|oo)o). a(6) = 6: (oooooo), (oo(oo|oo)), (o(oo|oo)o), ((oo|oo)oo), (o(oo|ooo)), ((oo|ooo)o). PROG (PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)} seq(n)={my(p=O(x^2)); for(n=2, n, p=x+x*Ser(EulerT(Vec(p, 1-n))); p=p^2/(1+p)); Vec(p, -n)} CROSSREFS Cf. A003430, A339151, A339155, A339156. Sequence in context: A131244 A077926 A091601 * A063119 A218982 A106803 Adjacent sequences:  A339151 A339152 A339153 * A339155 A339156 A339157 KEYWORD nonn AUTHOR Andrew Howroyd, Nov 26 2020 STATUS approved

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Last modified August 9 18:55 EDT 2022. Contains 356026 sequences. (Running on oeis4.)