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 A144187 #17 Feb 16 2025 08:33:09
%S A144187 1,1,1,6,12,20,60,1680,4032,181440,907200,2851200,17107200,62270208,
%T A144187 242161920,29059430400,232475443200,1077840691200,277159034880,
%U A144187 52660216627200,283555012608000,65501207912448000,720513287036928000
%N A144187 Denominators of series expansion of the e.g.f. for the Catalan numbers.
%H A144187 G. C. Greubel, <a href="/A144187/b144187.txt">Table of n, a(n) for n = 0..480</a>
%H A144187 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>
%F A144187 E.g.f.: exp(2*x)*(BesselI(0, 2*x) - BesselI(1, 2*x)).
%e A144187 E.g.f. = 1 + x + x^2 + (5*x^3)/6 + (7*x^4)/12 + ...
%p A144187 seq(denom(binomial(2*n,n)/(n+1)!),n=0..30); # _Vladeta Jovovic_, Dec 03 2008
%t A144187 With[{m = 30}, CoefficientList[Series[Exp[2*x]*(BesselI[0, 2*x] - BesselI[1, 2*x]), {x, 0, m}], x]]//Denominator (* _G. C. Greubel_, Jan 17 2019 *)
%o A144187 (PARI) vector(30, n, n--; denominator(binomial(2*n,n)/(n+1)!)) \\ _G. C. Greubel_, Jan 17 2019
%o A144187 (Magma) [Denominator(Binomial(2*n,n)/Factorial(n+1)): n in [0..30]]; // _G. C. Greubel_, Jan 17 2019
%o A144187 (Sage) [denominator(binomial(2*n,n)/factorial(n+1)) for n in (0..30)] # _G. C. Greubel_, Jan 17 2019
%Y A144187 Cf. A000108, A144186.
%K A144187 nonn,frac
%O A144187 0,4
%A A144187 _Eric W. Weisstein_, Sep 13 2008