A159992 Numerator of Sum_{k=0..n} A159990(k)/A159991(k).

1, 41, 4927, 49277, 5913251, 33262037, 31931555539, 127726222157, 4598143997653, 306542933176867, 827665919577540943, 49659955174652456593, 744899327619786848909, 1862248319049467122273, 446939596571872109345521

Offset: 0

Author

Reinhard Zumkeller, May 01 2009

Keywords

• frac
• nonn

Comments

a(n)/A159993(n) approximates the positive root of x^3+2*x^2+10*x=20:

A159994(n)/A159995(n) = f(a(n)/A159993(n)) --> 0, where f(x) = x^3 + 2*x^2 + 10*x - 20;

a(n)/A159993(n) = a(n-1)/A159993(n-1) + A159990(n)/A159991(n).

Limit can be found at A202300. - Jason Bard, Jul 26 2025

Examples

			a(0)/A159993(0) = 1;
a(1)/A159993(1) = 41/30;
a(2)/A159993(2) = 4927/3600;
a(3)/A159993(3) = 49277/36000;
a(4)/A159993(4) = 5913251/4320000;
a(5)/A159993(5) = 33262037/24300000;
a(6)/A159993(6) = 31931555539/23328000000;
a(7)/A159993(7) = 127726222157/93312000000;
a(8)/A159993(8) = 4598143997653/3359232000000;
and written as decimal fractions:
a(0)/A159993(0) = 1;
a(1)/A159993(1) ~= 1.3666666666666667;
a(2)/A159993(2) ~= 1.3686111111111111;
a(3)/A159993(3) ~= 1.3688055555555556;
a(4)/A159993(4) ~= 1.3688081018518519;
a(5)/A159993(5) ~= 1.3688081069958847;
a(6)/A159993(6) ~= 1.3688081078103566;
a(7)/A159993(7) ~= 1.3688081078210733;
a(8)/A159993(8) ~= 1.3688081078213710.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..30

Crossrefs

Cf. A159990, A159991, A159993 (denominator), A159994, A159995, A202300.