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 A352303 #16 Aug 21 2024 11:23:58
%S A352303 1,-1,1,5,-47,239,-239,-11761,170689,-1237825,-2360159,238756319,
%T A352303 -4146035519,32586126143,359988680689,-18567245926321,351652342984321,
%U A352303 -2283764958280321,-89760640709677247,3866819337993369023,-74731210747948586879,167887841949213912959
%N A352303 Expansion of e.g.f. 1/(exp(x) - x^3).
%F A352303 a(n) = n * (n-1) * (n-2) * a(n-3) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
%F A352303 a(n) = n! * Sum_{k=0..floor(n/3)} (-k-1)^(n-3*k)/(n-3*k)!. - _Seiichi Manyama_, Aug 21 2024
%t A352303 m = 21; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^3), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352303 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^3)))
%o A352303 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
%o A352303 a(n) = b(n, 3);
%Y A352303 Cf. A089148, A352302, A352304.
%Y A352303 Cf. A352299.
%K A352303 sign
%O A352303 0,4
%A A352303 _Seiichi Manyama_, Mar 11 2022