

A120791


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


2



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

0,2


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.


LINKS



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.


EXAMPLE

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


CROSSREFS



KEYWORD

nonn,easy,frac


AUTHOR



STATUS

approved



