A120789 Numerators of partial sums of Catalan numbers scaled by powers of -1/8.

1, 7, 29, 459, 1843, 14723, 58925, 1885171, 7541399, 60328761, 241319243, 3861078495, 15444365983, 123554742139, 494219302861, 31630025688259, 126520120431871, 1012160898632573, 4048643713939967, 64778298539407877

Offset: 0

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy
• frac

Comments

From the expansion of sqrt(3/2) = 1+(1/4)*Sum_{k=0..oo} C(k)/(-8)^k one has, with the partial sums r(n) are defined below, r := lim_{n->oo} r(n) = 2*(sqrt(6)-2) = 0.898979485...

Denominators are given under A120781 (but may differ for higher n values).

Examples

			Rationals r(n): [1, 7/8, 29/32, 459/512, 1843/2048, 14723/16384,
58925/65536, 1885171/2097152, 7541399/8388608,...].
		

Links

• W. Lang: Rationals r(n) and limit.

Formula

a(n)=numerator(r(n)), with the rationals r(n):=Sum_{k=0..n} ((-1)^k)*C(k)/8^k with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.