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 A351275 #13 Feb 16 2025 08:34:02
%S A351275 1,-2,18,-268,5580,-149368,4887368,-189010176,8434813760,
%T A351275 -426626153664,24118046539968,-1507010218083456,103135804627122816,
%U A351275 -7672260068001952512,616407170000568900864,-53192668792451354284032,4906864974307552234844160
%N A351275 a(n) = Sum_{k=0..n} (-2*k)^k * Stirling1(n,k).
%H A351275 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A351275 E.g.f.: 1/(1 + LambertW( 2 * log(1+x) )), where LambertW() is the Lambert W-function.
%F A351275 a(n) ~ (-1)^n * exp(-1/2 - n + n*exp(-1)/2) * n^n / (sqrt(2) * (exp(exp(-1)/2) - 1)^(n+1/2)). - _Vaclav Kotesovec_, Feb 06 2022
%o A351275 (PARI) a(n) = sum(k=0, n, (-2*k)^k*stirling(n, k, 1));
%o A351275 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(2*log(1+x)))))
%Y A351275 Cf. A351274, A351277.
%K A351275 sign
%O A351275 0,2
%A A351275 _Seiichi Manyama_, Feb 05 2022