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 A112697 #15 Sep 07 2022 09:04:15
%S A112697 1,4,22,157,1291,11497,107725,1045948,10428178,106126924,1097913928,
%T A112697 11511677470,122057782762,1306480339462,14098243951822,
%U A112697 153208673236237,1675240428936307,18417589741637077,203464608460961377
%N A112697 Partial sum of Catalan numbers (A000108) multiplied by powers of 3.
%H A112697 Vincenzo Librandi, <a href="/A112697/b112697.txt">Table of n, a(n) for n = 0..300</a>
%F A112697 a(n) = Sum_{k=0..n} C(k)*3^k, n>=0, with C(n) = A000108(n).
%F A112697 G.f.: c(3*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers (A000108).
%F A112697 Recurrence: (n+1)*a(n) = (13*n-5)*a(n-1) - 6*(2*n-1)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F A112697 a(n) ~ 12^(n+1)/(11*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%t A112697 CoefficientList[Series[(1-Sqrt[1-12*x])/(6*x)/(1-x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%o A112697 (PARI) x='x+O('x^50); Vec((1-sqrt(1-12*x))/(6*x*(1-x))) \\ _G. C. Greubel_, Mar 17 2017
%Y A112697 Fourth column (m=3) of triangle A112705.
%Y A112697 Cf. A000108.
%K A112697 nonn,easy
%O A112697 0,2
%A A112697 _Wolfdieter Lang_, Oct 31 2005