A241994 Decimal expansion of lim_{n -> infinity} Product_{k=1..2n} (1 - 2/(2*k+1))^(k*(-1)^k).

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

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

J.-P. Allouche, A note on products involving zeta(3) and Catalan's constant. arXiv:1305.6247v3 [math.NT], 2014

Formula

exp(2*G/Pi - 1/2), where G is Catalan's constant (G = A006752 = 0.915965594...).

Example

1.08667416616077395213570672082096523329598330887030210204951841...

Mathematica

RealDigits[Exp[2*Catalan/Pi - 1/2] , 10, 105] // First

Prog

(PARI) default(realprecision, 100); exp(2*Catalan/Pi - 1/2) \\ G. C. Greubel, Aug 25 2018
(Magma) SetDefaultRealField(RealField(100)); R:=RealField(); Exp(2*Catalan(R)/Pi(R) - 1/2); // G. C. Greubel, Aug 25 2018

Crossrefs

Cf. A006752, A241992, A241993.

Sequence in context: A114141 A089139 A093209 * A275828 A154499 A329080

Adjacent sequences: A241991 A241992 A241993 * A241995 A241996 A241997

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 11 2014

Status

approved