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 A109581 #8 Nov 21 2024 18:02:37
%S A109581 0,1,-2,6,0,-120,1440,-10080,40320,362880,-10886400,159667200,
%T A109581 -1437004800,0,348713164800,-9153720576000,146459529216000,
%U A109581 -1067062284288000,-25609494822912000,1338096104497152000,-34060628114472960000,510909421717094400000
%N A109581 E.g.f.: x/(1+x-x^3).
%F A109581 D-finite with recurrence a(n) + n*a(n-1) - n*(n-1)*(n-2)*a(n-3) = 0. - _R. J. Mathar_, Aug 20 2021
%p A109581 G:=x/(1+x-x^3): Gser:=series(G,x=0,26): 0,seq(n!*coeff(Gser,x^n),n=1..23); # yields signed sequence
%t A109581 g[x_] = x/(-1 - x + x^3) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[h[x, n], {n, 0, 25}]; b = a[0]
%t A109581 With[{nn=30},CoefficientList[Series[x/(1+x-x^3),{x,0,nn}],x] Range[0,nn]!] (* _Harvey P. Dale_, Nov 21 2024 *)
%Y A109581 Sequence having -G as o.g.f. is A104769.
%K A109581 sign
%O A109581 0,3
%A A109581 _Roger L. Bagula_, Jun 29 2005