A120789 - OEIS

%I #10 Sep 14 2024 06:52:23

%S 1,7,29,459,1843,14723,58925,1885171,7541399,60328761,241319243,

%T 3861078495,15444365983,123554742139,494219302861,31630025688259,

%U 126520120431871,1012160898632573,4048643713939967,64778298539407877

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

%C 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...

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

%H W. Lang: <a href="/A120789/a120789.txt">Rationals r(n) and limit.</a>

%F 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.

%e Rationals r(n): [1, 7/8, 29/32, 459/512, 1843/2048, 14723/16384,

%e 58925/65536, 1885171/2097152, 7541399/8388608,...].

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006