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 A112702 #8 Jan 30 2024 16:18:06
%S A112702 1,9,137,2697,60041,1436297,36039305,935717513,24927136393,
%T A112702 677493729929,18712061405833,523679956331145,14818155751139977,
%U A112702 423231749888535177,12185543261045516937,353292577084597987977,10305591916877658319497
%N A112702 Partial sum of Catalan numbers A000108 multiplied by powers of 8.
%F A112702 a(n) = Sum_{k=0..n} C(k)*8^k, with C(n) = A000108(n).
%F A112702 G.f.: c(8*x)/(1-x), where c(x) = (1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
%F A112702 Conjecture: (n+1)*a(n) +3*(-11*n+5)*a(n-1) +16*(2*n-1)*a(n-2)=0. - _R. J. Mathar_, Jun 08 2016
%Y A112702 Column m=8 of triangle A112705.
%K A112702 nonn,easy
%O A112702 0,2
%A A112702 _Wolfdieter Lang_, Oct 31 2005