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 A064093 #20 Sep 08 2022 08:45:04
%S A064093 1,1,11,221,5531,154941,4649451,146150061,4750427771,158361063581,
%T A064093 5384626548491,186023930383501,6511108452179611,230400987949757821,
%U A064093 8228844334672249131,296245683962814194541,10739133812893020645051
%N A064093 Generalized Catalan numbers C(10; n).
%C A064093 a(n+1) = Y_{n}(n+1) = Z_{n}, n >= 0, in the Derrida et al. 1992 reference (see A064094) for alpha=10, beta =1 (or alpha=1, beta=10).
%C A064093 In general, for m>=1, C(m; n) ~ m * (4*m)^n / ((2*m - 1)^2 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Jun 10 2019
%H A064093 G. C. Greubel, <a href="/A064093/b064093.txt">Table of n, a(n) for n = 0..620</a>
%F A064093 G.f.: (1 + 10*x*c(10*x)/9)/(1+x/9) = 1/(1 - x*c(10*x)) with c(x) g.f. of Catalan numbers A000108.
%F A064093 a(n) = Sum_{m=0..n-1} (n-m)*binomial(n-1+m, m)*(10^m)/n.
%F A064093 a(n) = (-1/9)^n*(1 - 10*Sum_{k=0..n-1} C(k)*(-90)^k ), n >= 1, a(0) := 1; with C(n)=A000108(n) (Catalan).
%F A064093 a(n) = Sum_{k=0..n} A059365(n, k)*10^(n-k). - _Philippe Deléham_, Jan 19 2004
%F A064093 a(n) ~ 2^(3*n + 1) * 5^(n+1) / (361*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Jun 10 2019
%t A064093 CoefficientList[Series[(19 -Sqrt[1-40*x])/(2*(x+9)), {x, 0, 20}], x] (* _G. C. Greubel_, May 02 2019 *)
%o A064093 (PARI) my(x='x+O('x^20)); Vec((19 -sqrt(1-40*x))/(2*(x+9))) \\ _G. C. Greubel_, May 02 2019
%o A064093 (Magma) R<x>:=PowerSeriesRing(Rationals(), 20); Coefficients(R!( (19 - Sqrt(1-40*x))/(2*(x+9)) )); // _G. C. Greubel_, May 02 2019
%o A064093 (Sage) ((19 -sqrt(1-40*x))/(2*(x+9))).series(x, 20).coefficients(x, sparse=False) # _G. C. Greubel_, May 02 2019
%Y A064093 Cf. A064092 (C(9, n)).
%Y A064093 Cf. A000108, A059365.
%K A064093 nonn,easy
%O A064093 0,3
%A A064093 _Wolfdieter Lang_, Sep 13 2001