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 A362493 #12 Feb 16 2025 08:34:05
%S A362493 1,1,1,-1,-31,-319,-2279,-4199,269473,7155233,114846641,920526641,
%T A362493 -18415853279,-1115017249631,-31675298017271,-526379460621559,
%U A362493 2394778195929281,603748739138745281,27895091311964499553,769764386129113157473,6164705700089328588481
%N A362493 E.g.f. satisfies A(x) = exp(x - x^3/3 * A(x)^3).
%H A362493 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A362493 E.g.f.: exp(x - LambertW(x^3 * exp(3*x))/3) = ( LambertW(x^3 * exp(3*x))/x^3 )^(1/3).
%F A362493 a(n) = n! * Sum_{k=0..floor(n/3)} (-1/3)^k * (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).
%o A362493 (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(x^3*exp(3*x))/3)))
%Y A362493 Cf. A362492, A362494.
%Y A362493 Cf. A362478.
%K A362493 sign
%O A362493 0,5
%A A362493 _Seiichi Manyama_, Apr 22 2023