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 A367789 #14 Feb 16 2025 08:34:06
%S A367789 1,1,9,106,1697,35076,893947,27165706,960298593,38751082552,
%T A367789 1758831242291,88726543365054,4926355857050641,298605321687360676,
%U A367789 19623211558172733435,1389870724939251455506,105556814502357807727553,8557797733469700008170224
%N A367789 E.g.f. satisfies A(x) = exp( x/(1-x)^3 * A(x) ).
%H A367789 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A367789 E.g.f.: exp( -LambertW(-x/(1-x)^3) ).
%F A367789 a(n) = n! * Sum_{k=0..n} (k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!.
%p A367789 A367789 := proc(n)
%p A367789 n!*add((k+1)^(k-1) * binomial(n+2*k-1,n-k)/k!,k=0..n) ;
%p A367789 end proc:
%p A367789 seq(A367789(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A367789 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-x/(1-x)^3))))
%Y A367789 Cf. A052868, A362775, A367790.
%Y A367789 Cf. A091695, A360100.
%K A367789 nonn
%O A367789 0,3
%A A367789 _Seiichi Manyama_, Nov 30 2023