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 A382000 #14 Mar 22 2025 10:56:42
%S A382000 1,1,14,342,12872,659280,42828912,3375009568,312860626304,
%T A382000 33361836534144,4023352486200320,541461682626399744,
%U A382000 80448618080927609856,13079749459734097573888,2309915877337042992324608,440332184936376095626076160,90117169223076699520606896128
%N A382000 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^5.
%F A382000 a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A002294(k)/(n-k)!.
%F A382000 a(n) ~ 2^(n-3) * n^(n-1) * sqrt(5*(1 + LambertW(512/3125))) / (exp(n) * LambertW(512/3125)^n). - _Vaclav Kotesovec_, Mar 22 2025
%o A382000 (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(5*k+1, k)/((5*k+1)*(n-k)!));
%Y A382000 Cf. A336950, A381997, A381998, A381999, A382001.
%Y A382000 Cf. A002294, A377526, A381986.
%K A382000 nonn
%O A382000 0,3
%A A382000 _Seiichi Manyama_, Mar 12 2025