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 A116867 #8 May 25 2021 10:30:40 %S A116867 1,2,9,58,446,3792,34369,325538,3184206,31917772,326156474,3385065348, %T A116867 35585008816,378116619692,4054571715729,43820012675698, %U A116867 476830454211926,5219833626494412,57444768682580494,635176593108262028 %N A116867 Convolution of generalized Catalan sequence A064063 (named C(3;n)). %C A116867 Row sums of generalized Catalan triangle A116866 (named C(1,3)). %H A116867 J. Abate, W. Whitt, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Whitt/whitt6.html">Brownian Motion and the Generalized Catalan Numbers</a>, J. Int. Seq. 14 (2011) # 11.2.6, example after (34). %F A116867 a(n)=sum(A116866(n,m),m=0..n), n>=0. %F A116867 G.f.: ((1+3*x*c(3*x)/2)/(1+x/2))^2 = (4-3*x + 15*x*c(3*x))/(2+x)^2, with the o.g.f. c(x) of A000108 (Catalan numbers). %F A116867 a(n)= sum(C(3;n-k)*C(3;k),k=0..n), n>=0, with C(3;n):= A064063(n). %F A116867 2*n*a(n) +(-23*n+37)*a(n-1) +6*(-2*n+1)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017 %K A116867 nonn,easy %O A116867 0,2 %A A116867 _Wolfdieter Lang_, Mar 24 2006