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 A371044 #10 Mar 10 2024 08:19:49
%S A371044 1,0,0,6,24,60,120,5250,80976,726264,4839120,86487390,2283242280,
%T A371044 42585905076,590667519624,10115535833130,286758920451360,
%U A371044 8128299117822960,186279550983756576,4123388294626654134,118916807955913504440,4102548791571529697580
%N A371044 E.g.f. satisfies A(x) = 1 + x^3*exp(x*A(x)).
%F A371044 a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-3*k+1,k)/( (n-3*k+1)*(n-3*k)! ).
%t A371044 nmax = 20; CoefficientList[Series[1 - LambertW[-E^x*x^4]/x, {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Mar 10 2024 *)
%o A371044 (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-3*k+1, k)/((n-3*k+1)*(n-3*k)!));
%Y A371044 Cf. A370985, A371019, A371045, A371046.
%Y A371044 Cf. A161631, A371042.
%K A371044 nonn
%O A371044 0,4
%A A371044 _Seiichi Manyama_, Mar 09 2024