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 A351274 #21 Feb 16 2025 08:34:02
%S A351274 1,2,14,172,2964,65848,1789688,57521280,2133964352,89744964288,
%T A351274 4219022123328,219246630903936,12479659844383104,772174659456713472,
%U A351274 51603153976362554112,3704166182571098222592,284239227254465994240000,23218955083323248158556160
%N A351274 a(0) = 1; thereafter a(n) = Sum_{k=1..n} (2*k)^k * Stirling1(n,k).
%H A351274 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A351274 E.g.f.: 1/(1 + LambertW( -2 * log(1+x) )), where LambertW() is the Lambert W-function.
%F A351274 a(n) ~ n^n / (sqrt(2) * (exp(exp(-1)/2) - 1)^(n+1/2) * exp(n - exp(-1)/4 + 1/2)). - _Vaclav Kotesovec_, Feb 06 2022
%t A351274 Join[{1},Table[Sum[(2k)^k StirlingS1[n,k],{k,n}],{n,20}]] (* _Harvey P. Dale_, Dec 31 2023 *)
%o A351274 (PARI) a(n) = sum(k=0, n, (2*k)^k*stirling(n, k, 1));
%o A351274 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(-2*log(1+x)))))
%Y A351274 Cf. A305819, A351182, A351275, A351276.
%K A351274 nonn
%O A351274 0,2
%A A351274 _Seiichi Manyama_, Feb 05 2022
%E A351274 Made a(0) = 1 explicit and changed range of k in definition to start at 1 at the suggestion of _Harvey P. Dale_. - _N. J. A. Sloane_, Dec 31 2023