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 A058386 Essentially series series-parallel networks with n unlabeled edges, multiple edges not allowed. 2
 0, 0, 1, 1, 2, 4, 9, 20, 47, 112, 274, 678, 1709, 4346, 11176, 28966, 75656, 198814, 525496, 1395758, 3723986, 9975314, 26817655, 72332320, 195679137, 530814386, 1443556739, 3934880554, 10748839215, 29420919456, 80678144437, 221618678694 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS S. R. Finch, Series-parallel networks S. R. Finch, Series-parallel networks, July 7, 2003. [Cached copy, with permission of the author] J. W. Moon, Some enumerative results on series-parallel networks, Annals Discrete Math., 33 (1987), 199-226 (the sequence r_n). FORMULA G.f. satisfies A(x) = A058385(x) - x + x^2. MATHEMATICA (* f = g.f. of A058385 *) max = 31; f[x_] := Sum[b[n]*x^n, {n, 0, max}]; b[0] = 0; b[1] = 1; b[2] = 0; b[3] = 1; coef = CoefficientList[ Series[1 - x + x^2 + 2*f[x] - Product[(1 - x^j)^(-b[j]), {j, 1, max}], {x, 0, max}], x][[ 5 ;; All]]; g[x_] := Sum[a[n]*x^n, {n, 0, max}]; a[0] = a[1] = 0; a[2] = a[3] = 1; coeg = CoefficientList[ Series[g[x] - f[x] + x - x^2, {x, 0, max}], x][[ 5 ;; All]]; solf = SolveAlways[ Thread[coef == 0], x] ; solg = SolveAlways[ Thread[coeg == 0] /. solf[[1]], x]; Table[a[n], {n, 0, max}] /. solg[[1]] (* Jean-François Alcover, Jul 18 2012 *) terms = 32; (* f = g.f. of A058385 *) f[_] = 0; Do[f[x_] = (1/2)*(-1 + x - x^2 + Product[(1 - x^j)^(-Ceiling[Coefficient[f[x], x, j]]), {j, 1,  terms}]) + O[x]^ terms // Normal, 4*terms]; A[x_] = f[x] - x + x^2 + O[x]^terms; CoefficientList[A[x], x] (* Jean-François Alcover, Jan 10 2018 *) CROSSREFS Cf. A058379, A058385, A058387. Sequence in context: A035084 A213905 A058385 * A095980 A036619 A036620 Adjacent sequences:  A058383 A058384 A058385 * A058387 A058388 A058389 KEYWORD nonn,easy,nice AUTHOR N. J. A. Sloane, Dec 20 2000 STATUS approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)