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 A053533 #10 Sep 08 2022 08:45:00
%S A053533 1,0,0,0,0,12,60,360,2520,20160,199584,2147040,25043040,315485280,
%T A053533 4274281440,62237343168,968728662720,16046598597120,281802435747840,
%U A053533 5229395457937920,102253297006250496,2101387824575550720,45281611027331723520
%N A053533 Expansion of e.g.f.: (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6 -x^4/8).
%D A053533 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.15(a), k=5.
%H A053533 G. C. Greubel, <a href="/A053533/b053533.txt">Table of n, a(n) for n = 0..445</a>
%F A053533 a(n) ~ sqrt(2) * n^n / exp(n+25/24). - _Vaclav Kotesovec_, Aug 04 2014
%t A053533 With[{m = 30}, CoefficientList[Series[(1-x)^(-1/2)*Exp[-x/2 -x^2/4 -x^3/6 -x^4/8], {x, 0, m}], x]*Range[0, m]!] (* _G. C. Greubel_, May 15 2019 *)
%o A053533 (PARI) my(x='x+O('x^30)); Vec(serlaplace( (1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6 -x^4/8) )) \\ _G. C. Greubel_, May 15 2019
%o A053533 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( (1-x)^(-1/2)*Exp(-x/2 -x^2/4 -x^3/6 -x^4/8) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 15 2019
%o A053533 (Sage) m = 30; T = taylor((1-x)^(-1/2)*exp(-x/2 -x^2/4 -x^3/6 -x^4/8), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, May 15 2019
%Y A053533 Cf. A001205, A053532.
%K A053533 nonn
%O A053533 0,6
%A A053533 _N. J. A. Sloane_, Jan 16 2000