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 A120784 #6 Aug 30 2019 03:43:17 %S A120784 1,17,137,4389,35119,561925,4495433,287708141,2301665843,36826655919, %T A120784 294613251551,9427624079025,75420992684203,1206735883132973, %U A120784 9653887065398089,1235697544380650237 %N A120784 Numerators of partial sums of Catalan numbers scaled by powers of 1/16. %C A120784 Denominators are given under A120785. %C A120784 From the expansion of sqrt(3)/2 = sqrt(1-1/4) = 1-(1/8)*sum(C(k)/16^k,k=0..infinity) one has r:=limit(r(n),n to infinity)= 4*(2 - sqrt(3)) = 1.071796769..., with the partial sums r(n) defined below. %H A120784 W. Lang: <a href="/A120784/a120784.txt">Rationals r(n) and limit.</a> %F A120784 a(n)=numerator(r(n)), with the rationals r(n):=sum(C(k)/16^k,k=0..n) with C(k):=A000108(k) (Catalan numbers). Rationals r(n) are taken in lowest terms. %e A120784 Rationals r(n): [1, 17/16, 137/128, 4389/4096, 35119/32768, 561925/524288, 4495433/4194304, 287708141/268435456,...]. %K A120784 nonn,easy,frac %O A120784 0,2 %A A120784 _Wolfdieter Lang_, Jul 20 2006