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 A361194 #15 Feb 16 2025 08:34:05
%S A361194 1,-2,17,-237,4893,-133683,4567905,-187666587,9017657433,
%T A361194 -496470972951,30824023641669,-2131090659947439,162397790115179733,
%U A361194 -13525005928296072915,1222285110682680848169,-119135392516302191619507,12458374493322416970025521
%N A361194 E.g.f. satisfies A(x) = exp( -3*x*A(x) ) / (1-x).
%H A361194 Winston de Greef, <a href="/A361194/b361194.txt">Table of n, a(n) for n = 0..338</a>
%H A361194 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A361194 a(n) = n! * Sum_{k=0..n} (-3)^k * (k+1)^(k-1) * binomial(n,k)/k!.
%F A361194 E.g.f.: LambertW( 3*x/(1-x) ) / (3*x).
%o A361194 (PARI) a(n) = n!*sum(k=0, n, (-3)^k*(k+1)^(k-1)*binomial(n, k)/k!);
%o A361194 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(3*x/(1-x))/(3*x)))
%Y A361194 Cf. A352410, A352448, A361182, A361193.
%Y A361194 Cf. A361069.
%K A361194 sign
%O A361194 0,2
%A A361194 _Seiichi Manyama_, Mar 03 2023