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 A001572 Related to series-parallel networks. (Formerly M2500 N0989) 2
 1, 1, 1, 1, 3, 5, 17, 41, 127, 365, 1119, 3413, 10685, 33561, 106827, 342129, 1104347, 3584649, 11701369, 38374065, 126395259, 417908329, 1386618307, 4615388353, 15407188529, 51569669429, 173033992311, 581905285089, 1961034571967 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS From Gary W. Adamson, Sep 27 2008: (Start) Starting (1, 1, 1, 3, 5, 17, ...) = the INVERTi transform of A000084: (1, 2, 4, 10, 24, 66, ...). Equals left border of triangle A144962. (End) REFERENCES J. Riordan and C. E. Shannon, The number of two-terminal series-parallel networks, J. Math. Phys., 21 (1942), 83-93. Reprinted in Claude Elwood Shannon: Collected Papers, edited by N. J. A. Sloane and A. D. Wyner, IEEE Press, NY, 1993, pp. 560-570. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS J. Riordan and C. E. Shannon, The number of two-terminal series-parallel networks (annotated scanned copy) FORMULA G.f.: 1 - Sum_{k>=1} a(k)*x^k = Product_{n>=1} (1-x^n)^A000669(n). MATHEMATICA max = 29; (* b = A000669 *) b[1] = 1; b[n_] := Module[{s}, s = Series[1/(1 - x), {x, 0, n}]; Do[s = Series[s/(1 - x^k)^Coefficient[s, x^k], {x, 0, n}], {k, 2, n}]; Coefficient[s, x^n]/2]; gf = 2 - Product[(1 - x^n)^b[n], {n, 1, max}] + O[x]^max; CoefficientList[gf, x] (* Jean-François Alcover, Oct 23 2016 *) CROSSREFS Cf. A000084, A144962. - Gary W. Adamson, Sep 27 2008 Sequence in context: A336380 A113275 A280080 * A236458 A131342 A005142 Adjacent sequences:  A001569 A001570 A001571 * A001573 A001574 A001575 KEYWORD nonn,easy,changed AUTHOR STATUS approved

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Last modified June 13 00:04 EDT 2021. Contains 344980 sequences. (Running on oeis4.)