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 A064346 #8 Aug 09 2017 12:32:55 %S A064346 1,1,16,1216,157696,25317376,4543676416,873117515776,175715349692416, %T A064346 36562356662173696,7802094251017240576,1698089607837490610176, %U A064346 375493988522687218057216,84121868091432283370684416 %N A064346 Generalized Catalan numbers C(8,8; n). %C A064346 See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references. %H A064346 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, corollary 6. %F A064346 a(n)= ((8^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/8)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1). %F A064346 G.f.:(1-15*x*c(64*x))/(1-8*x*c(64*x))^2 = c(64*x)*(15+49*c(64*x))/(1+7*c(64*x))^2 = (15*c(64*x)*(8*x)^2+7*(7+23*x))/(7+8*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108. %F A064346 7*(-n+1)*a(n) +8*(223*n-560)*a(n-1) +1024*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017 %Y A064346 A064345. %K A064346 nonn,easy %O A064346 0,3 %A A064346 _Wolfdieter Lang_, Oct 12 2001