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 A053502 #20 Sep 08 2022 08:45:00
%S A053502 1,1,2,6,24,96,576,3312,21456,152784,1237536,9984096,133494912,
%T A053502 1412107776,16369357824,206123325696,2866280276736,36809077162752,
%U A053502 592066290710016,8800038127378944,136876273991755776,2197453620220010496,37915306084793106432
%N A053502 Number of degree-n permutations of order dividing 12.
%D A053502 R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10.
%H A053502 Alois P. Heinz, <a href="/A053502/b053502.txt">Table of n, a(n) for n = 0..200</a>
%H A053502 L. Moser and M. Wyman, <a href="http://dx.doi.org/10.4153/CJM-1955-020-0">On solutions of x^d = 1 in symmetric groups</a>, Canad. J. Math., 7 (1955), 159-168.
%F A053502 E.g.f.: exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12).
%p A053502 a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,
%p A053502 add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 3, 4, 6, 12])))
%p A053502 end:
%p A053502 seq(a(n), n=0..25); # _Alois P. Heinz_, Feb 14 2013
%t A053502 a[n_]:= a[n] = If[n<0, 0, If[n==0, 1, Sum[Product[n-i, {i, 1, j-1}]*a[n-j], {j, {1, 2, 3, 4, 6, 12}}]]]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Apr 24 2014, after _Alois P. Heinz_ *)
%t A053502 With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^3/3 +x^4/4 +x^6/6 + x^12/12], {x, 0, m}], x]*Range[0, m]!] (* _G. C. Greubel_, May 15 2019 *)
%o A053502 (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12) )) \\ _G. C. Greubel_, May 15 2019
%o A053502 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12) )); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, May 15 2019
%o A053502 (Sage) m = 30; T = taylor(exp(x + x^2/2 + x^3/3 + x^4/4 + x^6/6 + x^12/12), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, May 15 2019
%Y A053502 Cf. A000085, A001470, A001472, A053495-A053505, A005388.
%Y A053502 Column k=12 of A008307.
%K A053502 nonn
%O A053502 0,3
%A A053502 _N. J. A. Sloane_, Jan 15 2000