A241995 Decimal expansion of the limit when n -> infinity of the product Product_{k=1..2n+1} (1 - 2/(2*k+1))^(k*(-1)^k).

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

Offset

1,1

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], 2013-2014.

Formula

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

Example

2.95388663933071695887144998329544153094277247511773635151375552...

Mathematica

RealDigits[Exp[2*Catalan/Pi + 1/2] , 10, 104] // 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, A241994.

Sequence in context: A160208 A248364 A021776 * A019708 A201397 A077124

Adjacent sequences: A241992 A241993 A241994 * A241996 A241997 A241998

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 11 2014

Status

approved