A120780 Numerators of partial sums of Catalan numbers scaled by powers of 1/8.

1, 9, 37, 597, 2395, 19181, 76757, 2456653, 9827327, 78621047, 314488387, 5031843585, 20127426343, 161019596469, 644078720181, 41221047786429, 164884208824551, 1319073735418803, 5276295061084887, 84420721860989787

Offset

0,2

Comments

Denominators are under A120781.

From the expansion of sqrt(2)/2 = sqrt(1-1/2) = 1-(1/4)*sum(C(k)/8^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 2*(2 - sqrt(2)) = 1.171572875..., with the partial sums r(n) defined below.

Links

Table of n, a(n) for n=0..19.

W. Lang: Rationals r(n) and limit.

Formula

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

Example

Rationals r(n): [1, 9/8, 37/32, 597/512, 2395/2048, 19181/16384,
76757/65536, 2456653/2097152,...].

Crossrefs

Sequence in context: A026686 A076174 A117085 * A071229 A071238 A213583

Adjacent sequences: A120777 A120778 A120779 * A120781 A120782 A120783

Keyword

nonn,easy,frac

Author

Wolfdieter Lang, Jul 20 2006

Status

approved