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 A361212 #19 Feb 16 2025 08:34:05
%S A361212 1,3,33,612,16353,576108,25306803,1334701854,82258866225,
%T A361212 5805344935368,461848917299499,40904277651802458,3992219566916292873,
%U A361212 425766991650939828828,49266876888419716251315,6147944525591645916094182,823045511075200872642258273
%N A361212 E.g.f. satisfies A(x) = exp( 3*x*A(x) / (1-x) ).
%H A361212 Winston de Greef, <a href="/A361212/b361212.txt">Table of n, a(n) for n = 0..327</a>
%H A361212 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A361212 a(n) = n! * Sum_{k=0..n} 3^k * (k+1)^(k-1) * binomial(n-1,n-k)/k!.
%F A361212 E.g.f.: exp ( -LambertW(-3*x/(1-x)) ).
%F A361212 E.g.f.: -(1-x)/(3*x) * LambertW(-3*x/(1-x)).
%o A361212 (PARI) a(n) = n!*sum(k=0, n, 3^k*(k+1)^(k-1)*binomial(n-1, n-k)/k!);
%o A361212 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-3*x/(1-x)))))
%o A361212 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-(1-x)/(3*x)*lambertw(-3*x/(1-x))))
%Y A361212 Cf. A052868, A360939.
%Y A361212 Cf. A361066, A361182.
%K A361212 nonn
%O A361212 0,2
%A A361212 _Seiichi Manyama_, Mar 04 2023