A130557 Numerators of partial sums of a series for 6*(5 - 4*Zeta(3)).

1, 10, 409, 10297, 8031, 394019, 9462581, 766743461, 8435956183, 1020884056543, 13272613316059, 2243198436149971, 2243285892433171, 2243347792046947, 305101392961615867, 88175602457796281563, 186150555360181760633

Offset: 2

Author

Wolfdieter Lang, Jul 13 2007

Keywords

• nonn
• frac
• easy

Comments

Denominators are given in A130558.

The rational sequence r(n) = 24*Sum_{j=2..n} 1/(j^3*(j^2-1)), n >= 2, tends, in the limit n->infinity, to 6*(5-4*Zeta(3)) which is approximately 1.15063433.

Examples

			Rationals r(n), n >= 2: 1, 10/9, 409/360, 10297/9000, 8031/7000, 394019/343000, ....
		

References

• Z. A. Melzak, Companion to concrete mathematics,( Vol.I), Wiley, New York, 1973, pp. 83-84.

Links

• W. Lang, Rationals and limit.

Crossrefs

Cf. A130551/A130552 with the limit (4/5)*Zeta(3).

Formula

a(n) = numerator(r(n)), n >= 2, with the rationals r(n) defined above.