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 A365035 #13 Feb 16 2025 08:34:06
%S A365035 1,1,3,1,-11,61,301,-6299,7561,903673,-9019079,-145636919,4305630781,
%T A365035 7516191541,-2037845181371,22442805921901,944219385367441,
%U A365035 -29922880660473359,-288352494154313999,32071808922904896913,-273044292430852251899
%N A365035 E.g.f. satisfies A(x) = exp(x * (1 + x/A(x))).
%H A365035 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A365035 E.g.f.: exp( x + LambertW(x^2*exp(-x)) ).
%F A365035 a(n) = n! * Sum_{k=1..n} (-n+k+1)^(k-1) * binomial(k,n-k)/k! for n>0.
%o A365035 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x+lambertw(x^2*exp(-x)))))
%Y A365035 Cf. A125500, A143768, A363354, A363529, A365036, A365037.
%Y A365035 Cf. A361090.
%K A365035 sign
%O A365035 0,3
%A A365035 _Seiichi Manyama_, Aug 17 2023