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 A377811 #10 Feb 16 2025 08:34:07
%S A377811 1,4,27,283,4217,82971,2041855,60475885,2096566449,83324680435,
%T A377811 3736041351311,186594364199277,10274269171279657,618386703880855339,
%U A377811 40393224245061185919,2846030947359659421901,215160957844217080056161,17373449685399138641312739,1492298627191467511376377999
%N A377811 E.g.f. satisfies A(x) = exp(x * A(x)) / (1 - x)^3.
%H A377811 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A377811 E.g.f.: exp( -LambertW(-x/(1-x)^3) )/(1-x)^3.
%F A377811 E.g.f.: -LambertW(-x/(1-x)^3)/x.
%F A377811 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2*k+2,n-k)/k!.
%o A377811 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))/(1-x)^3))
%o A377811 (PARI) a(n) = n!*sum(k=0, n, (k+1)^(k-1)*binomial(n+2*k+2, n-k)/k!);
%Y A377811 Cf. A352410, A377810.
%Y A377811 Cf. A082030, A367789, A377743.
%K A377811 nonn
%O A377811 0,2
%A A377811 _Seiichi Manyama_, Nov 08 2024