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 A360482 #12 Feb 16 2025 08:34:04
%S A360482 0,1,8,120,2848,92960,3868224,195810496,11680512512,802445898240,
%T A360482 62396469222400,5417515922441216,519519435065020416,
%U A360482 54535504354085687296,6219954774471102242816,765903524713482618101760,101269330068289021683564544,14310318526812295078276628480
%N A360482 E.g.f. satisfies A(x) = x * exp(x + 3 * A(x)).
%H A360482 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A360482 E.g.f.: A(x) = -LambertW(-3*x * exp(x))/3.
%F A360482 a(n) = Sum_{k=1..n} 3^(k-1) * k^(n-1) * binomial(n,k).
%F A360482 a(n) ~ sqrt(1 + LambertW(exp(-1)/3)) * n^(n-1) /(3 * exp(n) * LambertW(exp(-1)/3)^n). - _Vaclav Kotesovec_, Feb 17 2023
%o A360482 (PARI) my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(-3*x*exp(x))/3)))
%o A360482 (PARI) a(n) = sum(k=1, n, 3^(k-1)*k^(n-1)*binomial(n, k));
%Y A360482 Cf. A216857, A360481, A360483, A360484.
%K A360482 nonn
%O A360482 0,3
%A A360482 _Seiichi Manyama_, Feb 09 2023