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 A365055 #17 Feb 16 2025 08:34:06
%S A365055 1,1,8,121,2818,89006,3559504,172489948,9825889532,643567980808,
%T A365055 47654835126436,3936868360416476,358990055621209984,
%U A365055 35816155847478234424,3880967272702222156952,453886307361640406266456,56985342864303337121933584,7644651551838264804179619200
%N A365055 E.g.f. satisfies A(x) = exp( x * (1+x/2) * A(x)^3 ).
%H A365055 Seiichi Manyama, <a href="/A365055/b365055.txt">Table of n, a(n) for n = 0..331</a>
%H A365055 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A365055 E.g.f.: exp( -LambertW(-3*x * (1+x/2))/3 ).
%F A365055 a(n) = n! * Sum_{k=0..n} (1/2)^(n-k) * (3*k+1)^(k-1) * binomial(k,n-k)/k!.
%o A365055 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x*(1+x/2))/3)))
%Y A365055 Cf. A365053, A365054, A365056.
%Y A365055 Cf. A363478.
%K A365055 nonn
%O A365055 0,3
%A A365055 _Seiichi Manyama_, Aug 19 2023