A258234 - OEIS

A258234

Decimal expansion of a constant related to A107379.

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

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Limit n->infinity (Integral_{x=0..1} Product_{k=1..n} x^k*(1-x^k) dx)^(1/n) = Limit n->infinity (A258191(n)/A258192(n))^(1/n) = 1/A258234 = 0.18515528932235959464731321119795428527382236445907508398560553036... .

LINKS

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

StackExchange - Mathematica, No response to an infinite limit

FORMULA

Equals limit n->infinity A107379(n)^(1/n).

Equals limit n->infinity A173519(n)^(1/n).

EXAMPLE

5.4008719041181541524660911191042700520294...

MATHEMATICA

r^2/(r-1) /.FindRoot[-PolyLog[2, 1-r] == Log[r]^2, {r, E}, WorkingPrecision->117] (* Vaclav Kotesovec, Jun 11 2015 *)

CROSSREFS

Cf. A107379, A173519, A258191, A258192, A258268, A258788.