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A001572
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Related to series-parallel networks.
(Formerly M2500 N0989)
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2
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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
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OFFSET
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0,5
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COMMENTS
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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)
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REFERENCES
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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).
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LINKS
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FORMULA
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G.f.: 1 - Sum_{k>=1} a(k)*x^k = Product_{n>=1} (1-x^n)^A000669(n).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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