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 A360545 #19 Feb 16 2025 08:34:04
%S A360545 0,1,6,54,756,14580,358668,10736712,378823392,15395255280,
%T A360545 708217959600,36380741745744,2064234271203360,128214974795177088,
%U A360545 8652900673357097472,630483717450225530880,49330027417316557012992,4124992361928178722764544
%N A360545 E.g.f. satisfies A(x) = x * exp( 3*(x + A(x))/2 ).
%H A360545 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A360545 E.g.f.: A(x) = (-2/3) * LambertW(-3*x/2 * exp(3*x/2)).
%F A360545 a(n) = Sum_{k=1..n} (3*k/2)^(n-1) * binomial(n,k) = 3^(n-1) * A100526(n).
%F A360545 a(n) ~ sqrt(1 + LambertW(exp(-1))) * 3^(n-1) * n^(n-1) / (2^(n-1) * exp(n) * LambertW(exp(-1))^n). - _Vaclav Kotesovec_, Feb 17 2023
%o A360545 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-2*lambertw(-3*x/2*exp(3*x/2))/3)))
%o A360545 (PARI) a(n) = sum(k=1, n, (3*k/2)^(n-1)*binomial(n, k));
%Y A360545 Cf. A100526, A216857, A360548.
%Y A360545 Cf. A360482, A360544.
%K A360545 nonn
%O A360545 0,3
%A A360545 _Seiichi Manyama_, Feb 11 2023