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 A352310 #16 Aug 21 2024 11:23:16
%S A352310 1,-1,1,0,-7,39,-139,139,3249,-38305,257641,-724681,-9925519,
%T A352310 208718223,-2209932451,11619569779,98841199521,-3691083087521,
%U A352310 56488651405393,-466578080641297,-1989509977776479,159427986446212959,-3372599255892634459,39809520784433784075
%N A352310 Expansion of e.g.f. 1/(exp(x) - x^3/6).
%F A352310 a(n) = binomial(n,3) * a(n-3) - Sum_{k=1..n} binomial(n,k) * a(n-k) for n > 2.
%F A352310 a(n) = n! * Sum_{k=0..floor(n/3)} (-k-1)^(n-3*k)/(6^k*(n-3*k)!). - _Seiichi Manyama_, Aug 21 2024
%t A352310 m = 23; Range[0, m]! * CoefficientList[Series[1/(Exp[x] - x^3/6), {x, 0, m}], x] (* _Amiram Eldar_, Mar 12 2022 *)
%o A352310 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(exp(x)-x^3/6)))
%o A352310 (PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (-1+(k==m))*binomial(n, k)*b(n-k, m)));
%o A352310 a(n) = b(n, 3);
%Y A352310 Cf. A089148, A352309, A352311.
%Y A352310 Cf. A352303.
%K A352310 sign
%O A352310 0,5
%A A352310 _Seiichi Manyama_, Mar 11 2022