A395437 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.

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, 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, 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

Offset

1,1

Comments

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.

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).

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.

References

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

Links

Table of n, a(n) for n=1..105.

V. Ravelomanana and L. Thimonier, Asymptotic enumeration of cographs, Electronic Notes in Discrete Mathematics, 7 (2001), 58-61.

Example

3.56083930953894332952612917270966777526971390...

Crossrefs

Cf. A000084, A000669, A363064, A363065.

Sequence in context: A274792 A388508 A243589 * A390003 A178255 A154467

Adjacent sequences: A395432 A395434 A395435 * A395438 A395439 A395440

Keyword

nonn,cons

Author

Nathaniel Johnston, May 25 2026

Status

approved