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 A340473 #22 Jan 09 2021 07:52:23
%S A340473 1,1,1,7,13,321,31,42673,-214983,12251809,-156239909,6366130761,
%T A340473 -135725103227,5265915854785,-155145910919817,6318044844152161,
%U A340473 -232403136941014799,10299509100942804033,-446889500139353805773,21789892230658085847673,-1078684347590588362463619
%N A340473 a(n) = n! [x^n] W(-W(x))/(-W(x)), where W(x) is the Lambert W function.
%C A340473 Let LW(x) = W(-W(x))/(-W(x)) denote the function in the definition and let T(x) = -W(-x) be Euler's tree function A000169, and L(x) = W(-x)/(-x) the labeled tree function A000272, then LW(x) = L(W(x)), and TW(x) := -T(W(-x)) is A097174, and RW(x) := T(-W(-x)) is A207833.
%H A340473 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%p A340473 W := x -> LambertW(x): gf := W(-W(x))/(-W(x)):
%p A340473 ser := series(gf, x, 24): seq(n!*coeff(ser, x, n), n=0..20);
%t A340473 gf := -ProductLog[-ProductLog[x]]/ProductLog[x];
%t A340473 Range[0, 20]! CoefficientList[Series[gf, {x, 0, 20}], x]
%o A340473 (PARI) my(x='x+O('x^25)); Vec(serlaplace(lambertw(-lambertw(x))/(-lambertw(x)))) \\ _Michel Marcus_, Jan 09 2021
%Y A340473 Cf. A097174, A177885, A207833, A227176, A340474.
%Y A340473 Cf. A000169, A000272.
%K A340473 sign
%O A340473 0,4
%A A340473 _Peter Luschny_, Jan 08 2021