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 A380407 #16 Jun 14 2025 10:19:15
%S A380407 1,3,21,207,2697,43803,854685,19512615,510977937,15112457523,
%T A380407 498560461989,18160560320895,724240913035545,31394996915447883,
%U A380407 1470245245400432685,73987438021589516247,3982389565847576723745,228331703268783136636515,13894569264190369648271157
%N A380407 E.g.f. satisfies A(x) = exp( 3 * x * exp(x) * A(x)^(1/3) ).
%H A380407 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A380407 E.g.f.: B(x)^3, where B(x) is the e.g.f. of A273954.
%F A380407 E.g.f.: A(x) = exp( -3*LambertW(-x * exp(x)) ).
%F A380407 a(n) = 3 * Sum_{k=0..n} k^(n-k) * (k+3)^(k-1) * binomial(n,k).
%t A380407 terms = 19; A[_] = 0; Do[A[x_] = Exp[3*x*Exp[x]*A[x]^(1/3)] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* _Stefano Spezia_, Jun 14 2025 *)
%o A380407 (PARI) a(n) = 3*sum(k=0, n, k^(n-k)*(k+3)^(k-1)*binomial(n, k));
%Y A380407 Cf. A273954, A357247, A380406.
%K A380407 nonn
%O A380407 0,2
%A A380407 _Seiichi Manyama_, Jan 23 2025