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 A064345 #8 Aug 09 2017 12:32:06 %S A064345 1,1,14,833,83006,10213854,1404124008,206635997673,31844571309110, %T A064345 5073749573133710,829012595472718580,138151786440502006186, %U A064345 23390450962161609522028,4012173837912126230070832 %N A064345 Generalized Catalan numbers C(7,7; n). %C A064345 See triangle A064879 with columns m built from C(m,m; n), m >= 0, also for Derrida et al. and Liggett references. %H A064345 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 A064345 a(n)= ((7^(2*(n-1)))/(n-1))*sum((m+1)*(m+2)*binomial(2*(n-2)-m, n-2-m)*((1/7)^(m+1)), m=0..n-2), n >= 2, a(0) := 1=: a(1). %F A064345 G.f.:(1-13*x*c(49*x))/(1-7*x*c(49*x))^2 = c(49*x)*(13+36*c(49*x))/(1+6*c(49*x))^2 = (13*c(49*x)*(7*x)^2+12*(3+10*x))/(6+7*x)^2 with c(x)= A(x) g.f. of Catalan numbers A000108. %F A064345 6*(-n+1)*a(n) +7*(167*n-420)*a(n-1) +686*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Aug 09 2017 %Y A064345 A064344. %K A064345 nonn,easy %O A064345 0,3 %A A064345 _Wolfdieter Lang_, Oct 12 2001