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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved