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A120791 Numerators of partial sums of Catalan numbers scaled by powers of -1/20. 2

%I #6 Aug 30 2019 03:44:31

%S 1,19,191,1527,76357,1527119,15271223,1221697411,488678993,

%T 244339494069,2443394944889,97735797766167,977357977713673,

%U 3909431910817547,39094319108242331,6255091057316833991

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

%C 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....

%C Denominators are given under A120796.

%H W. Lang: <a href="/A120791/a120791.txt">Rationals r(n) and limit.</a>

%F 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.

%e Rationals r(n): [1, 19/20, 191/200, 1527/1600, 76357/80000,

%e 1527119/1600000, 15271223/16000000, 1221697411/1280000000,...]

%K nonn,easy,frac

%O 0,2

%A _Wolfdieter Lang_, Jul 20 2006

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