This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A120791 #6 Aug 30 2019 03:44:31 %S A120791 1,19,191,1527,76357,1527119,15271223,1221697411,488678993, %T A120791 244339494069,2443394944889,97735797766167,977357977713673, %U A120791 3909431910817547,39094319108242331,6255091057316833991 %N A120791 Numerators of partial sums of Catalan numbers scaled by powers of -1/20. %C A120791 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 A120791 Denominators are given under A120796. %H A120791 W. Lang: <a href="/A120791/a120791.txt">Rationals r(n) and limit.</a> %F A120791 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 A120791 Rationals r(n): [1, 19/20, 191/200, 1527/1600, 76357/80000, %e A120791 1527119/1600000, 15271223/16000000, 1221697411/1280000000,...] %K A120791 nonn,easy,frac %O A120791 0,2 %A A120791 _Wolfdieter Lang_, Jul 20 2006