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 A112700 #14 Jun 12 2024 21:26:39
%S A112700 1,7,79,1159,19303,345895,6504487,126597031,2528447911,51526205863,
%T A112700 1067116097959,22394503831975,475191351108007,10177980935594407,
%U A112700 219758235960500647,4778128782752211367,104526001924311998887
%N A112700 Partial sum of Catalan numbers A000108 multiplied by powers of 6.
%H A112700 Robert Israel, <a href="/A112700/b112700.txt">Table of n, a(n) for n = 0..727</a>
%F A112700 a(n) = Sum_{k=0..n} C(k)*6^k, with C(n):=A000108(n).
%F A112700 G.f.: c(6*x)/(1-x), where c(x):=(1-sqrt(1-4*x))/(2*x) is the o.g.f. of Catalan numbers A000108.
%F A112700 Conjecture: (n+1)*a(n) +(-25*n+11)*a(n-1) +12*(2*n-1)*a(n-2)=0. - _R. J. Mathar_, Jun 08 2016, verified by _Robert Israel_, Jun 28 2018
%F A112700 0 = a(n)*(+576*a(n+1) -636*a(n+2) +60*a(n+3)) +a(n+1)*(-564*a(n+1) +613*a(n+2) -61*a(n+3)) +a(n+2)*(+11*a(n+2) +a(n+3)) for all n>=0. - _Michael Somos_, Jun 28 2018
%p A112700 ListTools:-PartialSums([seq(binomial(2*n,n)/(n+1)*6^n,n=0..50)]); # _Robert Israel_, Jun 28 2018
%t A112700 Accumulate[Table[ (CatalanNumber@ n)*6^n, {n, 0, 16}]] (* _James C. McMahon_, Jun 11 2024 *)
%Y A112700 Seventh column (m=6) of triangle A112705.
%K A112700 nonn,easy
%O A112700 0,2
%A A112700 _Wolfdieter Lang_, Oct 31 2005