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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

Table of n, a(n) for n=0..28.

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-Fran├žois Alcover, Oct 23 2016 *)

CROSSREFS

Cf. A000084, A144962. - Gary W. Adamson, Sep 27 2008

Sequence in context: A141160 A113275 A280080 * A236458 A131342 A005142

Adjacent sequences:  A001569 A001570 A001571 * A001573 A001574 A001575

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 24 01:08 EDT 2018. Contains 316541 sequences. (Running on oeis4.)