A120791 Numerators of partial sums of Catalan numbers scaled by powers of -1/20.

1, 19, 191, 1527, 76357, 1527119, 15271223, 1221697411, 488678993, 244339494069, 2443394944889, 97735797766167, 977357977713673, 3909431910817547, 39094319108242331, 6255091057316833991

Offset: 0

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy
• frac

Comments

From the expansion of sqrt(1+1/5) = 1+(1/10)*sum(C(k)/(-20)^k,k=0..infinity) one has, with the partial sums r(n) are defined below, r:=limit(r(n),n to infinity)= (2*(sqrt(30)-5)) = 0.954451150....

Denominators are given under A120796.

Examples

			Rationals r(n): [1, 19/20, 191/200, 1527/1600, 76357/80000,
1527119/1600000, 15271223/16000000, 1221697411/1280000000,...]
		

Links

• W. Lang: Rationals r(n) and limit.

Formula

a(n)=numerator(r(n)), with the rationals r(n):=sum(((-1)^k)*C(k)/20^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms.