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 A351277 #12 Feb 16 2025 08:34:02
%S A351277 1,-2,14,-170,2910,-64202,1733278,-55338250,2039421598,-85204516298,
%T A351277 3979272245662,-205432301027978,11616783053131934,-714082744228546890,
%U A351277 47409028234931260318,-3380871137079666543114,257736986308003127354014
%N A351277 a(n) = Sum_{k=0..n} (-2*k)^k * Stirling2(n,k).
%H A351277 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A351277 E.g.f.: 1/(1 + LambertW( 2 * (exp(x) - 1) )), where LambertW() is the Lambert W-function.
%F A351277 a(n) ~ (-1)^n * n^n / (sqrt(2*exp(1) - 1) * exp(n) * (1 - log(exp(1) - 1/2))^(n + 1/2)). - _Vaclav Kotesovec_, Feb 06 2022
%o A351277 (PARI) a(n) = sum(k=0, n, (-2*k)^k*stirling(n, k, 2));
%o A351277 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(2*(exp(x)-1)))))
%Y A351277 Cf. A351218, A351275, A351276.
%K A351277 sign
%O A351277 0,2
%A A351277 _Seiichi Manyama_, Feb 05 2022