A146489 Decimal expansion of Product_{n>=2} (1 - 1/(n^3*(n-1))).

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

Offset

0,1

Comments

Product of Artin's constant of rank 3 and the equivalent almost-prime products.

Links

Zak Seidov, Table of n, a(n) for n = 0..999

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 = 3.

s*Sum_{j=1..floor(s/4)} binomial(s-3j-1, j-1)/j = A014097(s)-1.

Equals 1/Product_{k=1..4} Gamma(1-x_k), where x_k are the 4 roots of the polynomial x*(x+1)^3-1. [R. J. Mathar, Feb 20 2009]

Example

0.85067063079110435... = (1 - 1/8)*(1 - 1/54)*(1 - 1/192)*(1 - 1/500)*(1 - 1/1080)*...

Maple

r := 3 : ni := fsolve( (n+1)^r*n-1, n, complex) : 1.0/mul(GAMMA(1-d), d=ni) ; # R. J. Mathar, Feb 20 2009

Mathematica

p[k_] := Gamma[1 - Root[#^4 + 3#^3 + 3#^2 + # - 1&, k]]; RealDigits[1/(p[1]*p[2]*p[3]*p[4]) // Re, 10, 105] // First (* Jean-François Alcover, Feb 11 2013, after R. J. Mathar *)

Crossrefs

Cf. A065415.

Sequence in context: A361260 A300074 A096340 * A230162 A197841 A143347

Adjacent sequences: A146486 A146487 A146488 * A146490 A146491 A146492

Keyword

nonn,cons,easy

Author

R. J. Mathar, Feb 13 2009

Extensions

Offset in b-file corrected by N. J. A. Sloane, Aug 31 2009

Data extended by Jean-François Alcover, Feb 11 2013

Status

approved