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 A064344 #8 Aug 09 2017 12:31:15 %S A064344 1,1,12,540,39744,3598992,363776832,39348690624,4456429954560, %T A064344 521760612125952,62642882007530496,7670452375558388736, %U A064344 954216689151845302272,120261048050627578368000 %N A064344 Generalized Catalan numbers C(6,6; n). %C A064344 See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al.and Liggett references. %H A064344 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 A064344 a(n)= ((6^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/6)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1). %F A064344 G.f.:(1-11*x*c(36*x))/(1-6*x*c(36*x))^2 = c(36*x)*(11+25*c(36*x))/(1+5*c(36*x))^2 = (11*c(36*x)*(6*x)^2+5*(5+17*x))/(5+6*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108. %F A064344 5*(-n+1)*a(n) +6*(119*n-300)*a(n-1) +432*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017 %Y A064344 A064343. %K A064344 nonn,easy %O A064344 0,3 %A A064344 _Wolfdieter Lang_, Oct 12 2001