A340168 - OEIS

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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

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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]]