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 A330044 #13 Sep 08 2022 08:46:24
%S A330044 1,1,1,7,25,61,841,5251,20497,423865,3780721,20292031,559501801,
%T A330044 6487717237,44317795705,1527439916731,21798729916321,180816606476401,
%U A330044 7478345832314977,126737815733490295,1236785588298582841,59677199741873516461,1171057417377450325801
%N A330044 Expansion of e.g.f. exp(x) / (1 - x^3).
%H A330044 G. C. Greubel, <a href="/A330044/b330044.txt">Table of n, a(n) for n = 0..250</a>
%F A330044 G.f.: Sum_{k>=0} (3*k)! * x^(3*k) / (1 - x)^(3*k + 1).
%F A330044 a(0) = a(1) = a(2) = 1; a(n) = n * (n - 1) * (n - 2) * a(n - 3) + 1.
%F A330044 a(n) = Sum_{k=0..floor(n/3)} n! / (n - 3*k)!.
%F A330044 a(n) ~ n! * (exp(1)/3 + 2*cos(sqrt(3)/2 - 2*Pi*n/3) / (3*exp(1/2))). - _Vaclav Kotesovec_, Apr 18 2020
%F A330044 a(n) = A158757(n, 2*n). - _G. C. Greubel_, Dec 05 2021
%t A330044 nmax = 22; CoefficientList[Series[Exp[x]/(1 - x^3), {x, 0, nmax}], x] Range[0, nmax]!
%t A330044 Table[Sum[n!/(n - 3 k)!, {k, 0, Floor[n/3]}], {n, 0, 22}]
%o A330044 (Magma) [n le 3 select 1 else 1 + 6*Binomial(n-1,3)*Self(n-3): n in [1..41]]; // _G. C. Greubel_, Dec 05 2021
%o A330044 (Sage) [sum(factorial(3*k)*binomial(n, 3*k) for k in (0..n//3)) for n in (0..40)] # _G. C. Greubel_, Dec 05 2021
%Y A330044 Cf. A000522, A087208, A100732, A158757, A330045.
%K A330044 nonn
%O A330044 0,4
%A A330044 _Ilya Gutkovskiy_, Nov 28 2019