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 A378042 #8 Feb 16 2025 08:34:07
%S A378042 1,2,19,385,12041,512101,27616705,1806241151,138948411649,
%T A378042 12294333869545,1230146587626041,137347201671983227,
%U A378042 16928938651265737585,2283232081600363345037,334480117852142180147377,52888942867094899879009111,8978241760087200983202588545,1628601738501672908949881316433
%N A378042 E.g.f. satisfies A(x) = exp( x * A(x)^3 / (1-x) ) / (1-x).
%H A378042 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378042 E.g.f.: exp( -LambertW(-3*x/(1-x)^4)/3 )/(1-x).
%F A378042 a(n) = n! * Sum_{k=0..n} (3*k+1)^(k-1) * binomial(n+3*k,n-k)/k!.
%o A378042 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1-x)^4)/3)/(1-x)))
%o A378042 (PARI) a(n) = n!*sum(k=0, n, (3*k+1)^(k-1)*binomial(n+3*k, n-k)/k!);
%Y A378042 Cf. A377595, A378041.
%K A378042 nonn
%O A378042 0,2
%A A378042 _Seiichi Manyama_, Nov 15 2024