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 A375878 #17 Aug 05 2025 06:40:38
%S A375878 1,2,10,78,832,11320,187968,3693760,83970640,2170052928,62876256000,
%T A375878 2019782393904,71268840658464,2740911076718256,114134851494134352,
%U A375878 5116804468061982000,245747690114319479808,12589481527535031074304,685316177026591879217664
%N A375878 E.g.f. satisfies A(x) = 1/(1 - x)^(2*A(x)^(1/2)).
%H A375878 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A375878 E.g.f.: B(x)^2, where B(x) is the e.g.f. of A052813.
%F A375878 E.g.f.: exp( - 2*LambertW(log(1 - x)) ).
%F A375878 a(n) = 2 * Sum_{k=0..n} (k+2)^(k-1) * |Stirling1(n,k)|.
%F A375878 a(n) ~ 2 * n^(n-1) / ((exp(exp(-1)) - 1)^(n - 1/2) * exp(n - n*exp(-1) - 5/2)). - _Vaclav Kotesovec_, Aug 05 2025
%o A375878 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-2*lambertw(log(1-x)))))
%o A375878 (PARI) a(n) = 2*sum(k=0, n, (k+2)^(k-1)*abs(stirling(n, k, 1)));
%Y A375878 Cf. A052813, A375879.
%K A375878 nonn
%O A375878 0,2
%A A375878 _Seiichi Manyama_, Sep 01 2024