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 A370670 #9 Feb 25 2024 09:08:48
%S A370670 1,1,2,6,23,116,702,4945,39726,358596,3593759,39596032,475750740,
%T A370670 6190873441,86740653730,1301942638170,20842037779079,354469561697988,
%U A370670 6382795892548194,121310901632237857,2426864464216669694,50975856191753357928,1121692313538562441535
%N A370670 Expansion of Sum_{k>=0} k! * ( x/(1+x^3) )^k.
%F A370670 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * (n-3*k)! * binomial(n-2*k-1,k).
%F A370670 a(n) = n*a(n-1) + a(n-3) + (n-6)*a(n-4) + 2*a(n-6) for n > 6.
%o A370670 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*(x/(1+x^3))^k))
%o A370670 (PARI) a(n) = sum(k=0, n\3, (-1)^k*(n-3*k)!*binomial(n-2*k-1, k));
%Y A370670 Cf. A000255, A370669.
%Y A370670 Cf. A177251, A370508, A370511.
%K A370670 nonn
%O A370670 0,3
%A A370670 _Seiichi Manyama_, Feb 25 2024