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 A351276 #17 Feb 16 2025 08:34:02
%S A351276 1,2,18,266,5506,146602,4772162,183618794,8152995138,410307648938,
%T A351276 23079780216386,1434953808618090,97716253164212034,
%U A351276 7233006174407149866,578233606405444793410,49651123488091636885994,4557474786380802233761090,445324385454834015896585386
%N A351276 a(n) = Sum_{k=0..n} (2*k)^k * Stirling2(n,k).
%H A351276 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A351276 E.g.f.: 1/(1 + LambertW( 2 * (1 - exp(x)) )), where LambertW() is the Lambert W-function.
%F A351276 a(n) ~ n^n / (sqrt(1 + 2*exp(1)) * (log(exp(1) + 1/2) - 1)^(n + 1/2) * exp(n)). - _Vaclav Kotesovec_, Feb 06 2022
%o A351276 (PARI) a(n) = sum(k=0, n, (2*k)^k*stirling(n, k, 2));
%o A351276 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(2*(1-exp(x))))))
%Y A351276 Cf. A282190, A308490, A351274, A351277.
%K A351276 nonn
%O A351276 0,2
%A A351276 _Seiichi Manyama_, Feb 05 2022