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 A361193 #15 Feb 16 2025 08:34:05
%S A361193 1,-1,6,-50,648,-10952,232336,-5919664,176435328,-6024464000,
%T A361193 231972167424,-9946181374208,470038191434752,-24276240445152256,
%U A361193 1360508977539004416,-82233680186863536128,5332689963474238341120,-369321737420738845638656
%N A361193 E.g.f. satisfies A(x) = exp( -2*x*A(x) ) / (1-x).
%H A361193 Winston de Greef, <a href="/A361193/b361193.txt">Table of n, a(n) for n = 0..360</a>
%H A361193 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A361193 a(n) = n! * Sum_{k=0..n} (-2)^k * (k+1)^(k-1) * binomial(n,k)/k!.
%F A361193 E.g.f.: LambertW( 2*x/(1-x) ) / (2*x).
%o A361193 (PARI) a(n) = n!*sum(k=0, n, (-2)^k*(k+1)^(k-1)*binomial(n, k)/k!);
%o A361193 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(lambertw(2*x/(1-x))/(2*x)))
%Y A361193 Cf. A352410, A352448, A361182, A361194.
%Y A361193 Cf. A361068.
%K A361193 sign
%O A361193 0,3
%A A361193 _Seiichi Manyama_, Mar 03 2023