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 A356927 #20 Feb 16 2025 08:34:03
%S A356927 1,1,6,54,676,10980,220488,5289592,147828896,4721152320,169723566240,
%T A356927 6785559484704,298726260001728,14362141350822720,748845960914596608,
%U A356927 42092072779399215360,2537464961261745635328,163317885950059143238656
%N A356927 E.g.f. satisfies A(x) = 1/(1 - x)^(A(x)/(1 - x)).
%H A356927 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A356927 E.g.f.: A(x) = Sum_{k>=0} (k+1)^(k-1) * (-log(1-x)/(1-x))^k / k!.
%F A356927 E.g.f.: A(x) = exp( -LambertW(log(1-x)/(1-x)) ).
%F A356927 E.g.f.: A(x) = (1-x) * LambertW(log(1-x)/(1-x))/log(1-x).
%F A356927 a(n) ~ sqrt(1 + LambertW(exp(-1))) * n^(n-1) / (LambertW(exp(-1)) * exp(n - 1/2) * (1 - exp(1)*LambertW(exp(-1)))^(n - 1/2)). - _Vaclav Kotesovec_, Nov 14 2022
%o A356927 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(-log(1-x)/(1-x))^k/k!)))
%o A356927 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(log(1-x)/(1-x)))))
%o A356927 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace((1-x)*lambertw(log(1-x)/(1-x))/log(1-x)))
%Y A356927 Cf. A000254, A000272, A052813, A087761, A356925.
%K A356927 nonn
%O A356927 0,3
%A A356927 _Seiichi Manyama_, Sep 04 2022