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 A358493 #27 May 02 2024 04:28:40
%S A358493 1,1,2,7,26,126,745,5163,41052,367981,3669484,40282220,482650681,
%T A358493 6267119885,87659113950,1313921407891,21010208286486,356998222642362,
%U A358493 6423340164746737,122001442713615031,2439314857827015896,51212765334037840345,1126436834463405257528
%N A358493 a(n) = Sum_{k=0..floor(n/3)} (n-2*k)!/k!.
%H A358493 G. C. Greubel, <a href="/A358493/b358493.txt">Table of n, a(n) for n = 0..445</a>
%F A358493 a(n) = (n-1) * a(n-1) + (n-2) * a(n-2) + (n-4) * a(n-3) - 2 * a(n-4) - 2 * a(n-5) + 3 for n > 4.
%F A358493 a(n) ~ n! * (1 + 1/n^2 + 1/n^3 + 3/(2*n^4) + 4/n^5 + 41/(3*n^6) + 97/(2*n^7) + 1399/(8*n^8) + 3961/(6*n^9) + 322951/(120*n^10) + ...). - _Vaclav Kotesovec_, Nov 24 2022
%F A358493 G.f.: Sum_{k>=0} k! * x^k/(1-x^3)^(k+1). - _Seiichi Manyama_, Feb 26 2024
%t A358493 Table[Sum[(n-2*k)!/k!, {k,0,Floor[n/3]}], {n,0,30}] (* _G. C. Greubel_, May 01 2024 *)
%o A358493 (PARI) a(n) = sum(k=0, n\3, (n-2*k)!/k!);
%o A358493 (Magma)
%o A358493 [(&+[Factorial(n-2*k)/Factorial(k): k in [0..Floor(n/3)]]): n in [0..30]]; // _G. C. Greubel_, May 01 2024
%o A358493 (SageMath)
%o A358493 [sum(factorial(n-2*k)/factorial(k) for k in range(1+n//3)) for n in range(31)] # _G. C. Greubel_, May 01 2024
%Y A358493 Cf. A000522, A003470, A177251, A357949, A358494, A370511.
%K A358493 nonn,easy
%O A358493 0,3
%A A358493 _Seiichi Manyama_, Nov 19 2022