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 A053532 #14 Sep 08 2022 08:45:00
%S A053532 1,0,0,0,3,12,60,360,2835,24696,237384,2503440,28941165,363593340,
%T A053532 4930388892,71759200968,1115892704745,18465120087120,323965034820720,
%U A053532 6007037150742624,117377605956803571,2410702829834021820,51917379915449131020
%N A053532 Expansion of e.g.f.: (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6).
%D A053532 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(a), k=4.
%H A053532 G. C. Greubel, <a href="/A053532/b053532.txt">Table of n, a(n) for n = 0..445</a>
%F A053532 a(n) ~ sqrt(2) * n^n / exp(n+11/12). - _Vaclav Kotesovec_, Aug 04 2014
%F A053532 Conjecture: D-finite with recurrence 2*a(n) +2*(-n+1)*a(n-1) -(n-1)*(n-2)*(n-3)*a(n-4)=0. - _R. J. Mathar_, Jul 06 2020
%t A053532 With[{m = 30}, CoefficientList[Series[(1-x)^(-1/2)*Exp[-x/2 -x^2/4 -x^3/6], {x, 0, m}], x]*Range[0, m]!] (* _G. C. Greubel_, May 15 2019 *)
%o A053532 (PARI) my(x='x+O('x^30)); Vec(serlaplace( (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6) )) \\ _G. C. Greubel_, May 15 2019
%o A053532 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)^(-1/2)*Exp(-x/2 -x^2/4 -x^3/6) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 15 2019
%o A053532 (Sage) m = 30; T = taylor((1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, May 15 2019
%Y A053532 Cf. A001205, A053533.
%K A053532 nonn
%O A053532 0,5
%A A053532 _N. J. A. Sloane_, Jan 16 2000