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 A112699 #12 Mar 17 2017 21:59:35
%S A112699 1,6,56,681,9431,140681,2203181,35718806,594312556,10090406306,
%T A112699 174113843806,3044524000056,53828703687556,960689055250056,
%U A112699 17284175383375056,313147365080640681,5708299647795484431
%N A112699 Partial sum of Catalan numbers A000108 multiplied by powers of 5.
%H A112699 Vincenzo Librandi, <a href="/A112699/b112699.txt">Table of n, a(n) for n = 0..300</a>
%F A112699 a(n) = Sum_{k=0,..,n} C(k)*5^k, n>=0, with C(n):=A000108(n).
%F A112699 G.f.: c(5*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
%F A112699 Recurrence: (n+1)*a(n) = 3*(7*n-3)*a(n-1) - 10*(2*n-1)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A112699 a(n) ~ 20^(n+1)/(19*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%t A112699 CoefficientList[Series[(1-Sqrt[1-20*x])/(10*x)/(1-x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%o A112699 (PARI) x='x+O('x^50); Vec((1-sqrt(1-20*x))/(10*x*(1-x))) \\ _G. C. Greubel_, Mar 17 2017
%Y A112699 Sixth column (m=5) of triangle A112705.
%K A112699 nonn,easy
%O A112699 0,2
%A A112699 _Wolfdieter Lang_, Oct 31 2005