A340168 Decimal expansion of a constant related to the asymptotics of A004003.

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

Offset

1,4

Links

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

Formula

Equals lim_{n->infinity} A004003(n) / ((sqrt(2)-1)^(2*n) * exp(4*G*n*(n+1)/Pi)), where G is the Catalan's constant A006752.

Equals 2*exp(G/Pi) / (1 + sqrt(2)), where G is Catalan's constant A006752.

Example

1.1088622587807675132769511621308192926452661269635692243629431418447355653...

Mathematica

RealDigits[2*E^(Catalan/Pi)/(1 + Sqrt[2]), 10, 110][[1]]

Crossrefs

Cf. A004003, A007341, A007726, A065072, A127605, A340052.

Sequence in context: A153619 A202497 A195708 * A019704 A140976 A348372

Adjacent sequences: A340165 A340166 A340167 * A340169 A340170 A340171

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 30 2020

Status

approved