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%I M2500 N0989 #28 Jun 04 2021 22:42:46
%S 1,1,1,1,3,5,17,41,127,365,1119,3413,10685,33561,106827,342129,
%T 1104347,3584649,11701369,38374065,126395259,417908329,1386618307,
%U 4615388353,15407188529,51569669429,173033992311,581905285089,1961034571967
%N Related to series-parallel networks.
%C From _Gary W. Adamson_, Sep 27 2008: (Start)
%C Starting (1, 1, 1, 3, 5, 17, ...) = the INVERTi transform of A000084: (1, 2, 4, 10, 24, 66, ...).
%C Equals left border of triangle A144962. (End)
%D 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.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H J. Riordan and C. E. Shannon, <a href="/A000084/a000084_1.pdf">The number of two-terminal series-parallel networks</a> (annotated scanned copy)
%F G.f.: 1 - Sum_{k>=1} a(k)*x^k = Product_{n>=1} (1-x^n)^A000669(n).
%t 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 *)
%Y Cf. A000084, A144962. - _Gary W. Adamson_, Sep 27 2008
%K nonn,easy
%O 0,5
%A _N. J. A. Sloane_
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