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 A061137 #25 Sep 08 2022 08:45:03
%S A061137 0,0,1,3,6,30,270,1386,6048,46656,387180,2469060,17204616,158065128,
%T A061137 1903506696,18887563800,163657221120,2095170230016,30792968596368,
%U A061137 346564643468976,3905503235814240,58609511127871200,866032039742528736
%N A061137 Number of degree-n odd permutations of order dividing 6.
%H A061137 Robert Israel, <a href="/A061137/b061137.txt">Table of n, a(n) for n = 0..522</a>
%H A061137 Lev Glebsky, Melany Licón, Luis Manuel Rivera, <a href="https://arxiv.org/abs/1907.00548">On the number of even roots of permutations</a>, arXiv:1907.00548 [math.CO], 2019.
%H A061137 Robert Israel, <a href="/A061137/a061137.txt">Recurrence for this sequence</a>
%F A061137 E.g.f.: exp(x + x^3/3)*sinh(x^2/2 + x^6/6).
%F A061137 Linear recurrence of order 12 whose coefficients are polynomials in n of degree up to 15: see link. - _Robert Israel_, Jul 13 2018
%p A061137 Egf:= exp(x + x^3/3)*sinh(x^2/2 + x^6/6):
%p A061137 S:= series(Egf,x,31):
%p A061137 seq(coeff(S,x,j)*j!,j=0..30); # _Robert Israel_, Jul 13 2018
%t A061137 With[{m=30}, CoefficientList[Series[Exp[x + x^3/3]*Sinh[x^2/2 + x^6/6], {x, 0, m}], x]*Range[0,m]!] (* _Vincenzo Librandi_, Jul 02 2019 *)
%o A061137 (PARI) my(x='x+O('x^30)); concat([0,0], Vec(serlaplace( exp(x + x^3/3)*sinh(x^2/2 + x^6/6) ))) \\ _G. C. Greubel_, Jul 02 2019
%o A061137 (Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^3/3)*Sinh(x^2/2 + x^6/6) )); [0,0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // _G. C. Greubel_, Jul 02 2019
%o A061137 (Sage) m = 30; T = taylor(exp(x + x^3/3)*sinh(x^2/2 + x^6/6), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # _G. C. Greubel_, Jul 02 2019
%Y A061137 Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128, A000704, A061129-A061132, A048099, A051695, A061133-A061135, A001465, A061136-A061140.
%K A061137 easy,nonn
%O A061137 0,4
%A A061137 _Vladeta Jovovic_, Apr 14 2001