A395437 - OEIS

%I #17 May 29 2026 22:34:06

%S 3,5,6,0,8,3,9,3,0,9,5,3,8,9,4,3,3,2,9,5,2,6,1,2,9,1,7,2,7,0,9,6,6,7,

%T 7,7,5,2,6,9,7,1,3,9,0,2,5,8,0,1,3,9,6,5,4,3,2,8,3,1,9,8,1,6,5,1,6,7,

%U 7,8,4,8,9,2,6,7,5,8,4,9,1,4,4,9,9,6,2,3,3,3,0,7,1,7,1,9,0,5,4,4,3,5,4,0,5

%N Decimal expansion of 1/x, where x is the unique positive solution of f(x) = 1 and f(x) is the generating function of A000084.

%C Also the decimal expansion of 1/x, where x is the unique positive solution of g(x) = (1+x)/2 and g(x) is the generating function of A000669.

%C Since the generating function g satisfies 2*g(x)-x+1 = exp(Sum_{k>=1} g(x^k)/k), this constant is also the decimal expansion of the positive solution to Product_{n>=1} (1-1/x^n)^(-A000084(n)) = 2 (see A000084).

%C This constant is the growth rate of A000084 and A000669. That is, lim_{n->infinity} A000084(n+1)/A000084(n) equals this constant, and similarly for A000669. As a result, the growth rate of A363064 is bounded below by this constant.

%D J. Riordan and C. E. Shannon, The number of two-terminal series-parallel networks, Journal of Mathematics and Physics, 21 (1942), 83-93.

%H V. Ravelomanana and L. Thimonier, <a href="https://doi.org/10.1016/S1571-0653(04)00224-0">Asymptotic enumeration of cographs</a>, Electronic Notes in Discrete Mathematics, 7 (2001), 58-61.

%e 3.56083930953894332952612917270966777526971390...

%Y Cf. A000084, A000669, A363064, A363065.

%K nonn,cons

%O 1,1

%A _Nathaniel Johnston_, May 25 2026