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 A064329 #12 Sep 08 2022 08:45:04
%S A064329 1,1,-6,85,-1490,29226,-614004,13511709,-307448490,7174776190,
%T A064329 -170777485556,4130050311234,-101192982385844,2506610481299380,
%U A064329 -62668163792277840,1579300030107459885,-40076101342241993370
%N A064329 Generalized Catalan numbers C(-7; n).
%C A064329 See triangle A064334 with columns m built from C(-m; n), m >= 0, also for Derrida et al. references.
%H A064329 G. C. Greubel, <a href="/A064329/b064329.txt">Table of n, a(n) for n = 0..690</a>
%F A064329 a(n) = Sum_{m=0..n-1} (n-m)*binomial(n-1+m, m)*(-7)^m/n.
%F A064329 a(n) = (1/8)^n*(1 + 7*Sum_{k=0..n-1} C(k)*(-7*8)^k), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
%F A064329 G.f.: (1+7*x*c(-7*x)/8)/(1-x/8) = 1/(1-x*c(-7*x)) with c(x) g.f. of Catalan numbers A000108.
%t A064329 CoefficientList[Series[(15 +Sqrt[1+28*x])/(2*(8-x)), {x, 0, 30}], x] (* _G. C. Greubel_, May 03 2019 *)
%o A064329 (PARI) my(x='x+O('x^30)); Vec((15 +sqrt(1+28*x))/(2*(8-x))) \\ _G. C. Greubel_, May 03 2019
%o A064329 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( (15 +Sqrt(1+28*x))/(2*(8-x)) )); // _G. C. Greubel_, May 03 2019
%o A064329 (Sage) ((15 +sqrt(1+28*x))/(2*(8-x))).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 03 2019
%K A064329 sign,easy
%O A064329 0,3
%A A064329 _Wolfdieter Lang_, Sep 21 2001