A146492 Decimal expansion of Product_{n>=2} (1 - 1/(n^4*(n-1))).

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

Offset

0,1

Comments

Product of Artin's constant of rank 4 and the equivalent almost-prime products.

Links

Table of n, a(n) for n=0..104.

Formula

The logarithm is -Sum_{s>=2} Sum_{j=1..floor(s/(1+r))} binomial(s-r*j-1, j-1)*(1-Zeta(s))/j at r = 4.

s*Sum_{j=1..floor(s/5)} binomial(s-4j-1, j-1)/j = A058368(s)-1.

Equals 1/Product_{k=1..5} Gamma(1-x_k), where x_k are the 5 roots of the polynomial x*(x+1)^4-1. [R. J. Mathar, Feb 20 2009]

Example

0.9298384739543468522383.. = (1-1/16)*(1-1/162)*(1-1/768)*(1-1/2500)*..

Maple

r := 4 : ni := fsolve( (n+1)^r*n-1, n, complex) : 1.0/mul(GAMMA(1-d), d=ni) ; # R. J. Mathar, Feb 20 2009

Mathematica

g[k_] := Gamma[Root[-5 + 11# - 6#^2 + #^3 & , k]]; RealDigits[Cosh[(Sqrt[3] Pi)/2]/(Pi g[1] g[2] g[3]) // Re, 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)
RealDigits[Re[N[Product[1 - 1/(n^4 (n - 1)), {n, 2, Infinity}], 110]]] (* Bruno Berselli, Apr 02 2013 *)

Crossrefs

Cf. A065416.

Sequence in context: A200234 A242743 A197812 * A266565 A090298 A248315

Adjacent sequences: A146489 A146490 A146491 * A146493 A146494 A146495

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 13 2009

Extensions

More terms from Jean-François Alcover, Feb 12 2013

Status

approved