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 A381999 #14 Mar 22 2025 10:28:55
%S A381999 1,1,10,156,3656,115400,4595232,221281312,12510826624,812633118336,
%T A381999 59642105050880,4881685773730304,440905471531302912,
%U A381999 43559980305765793792,4673231270870843441152,541042726968231082967040,67236501012517546330062848,8927220151967826907452440576
%N A381999 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^3.
%F A381999 a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A001764(k)/(n-k)!.
%F A381999 a(n) ~ sqrt(3*(1 + LambertW(8/27))) * 2^(n - 3/2) * n^(n-1) / (exp(n) * LambertW(8/27)^n). - _Vaclav Kotesovec_, Mar 22 2025
%o A381999 (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(3*k+1, k)/((3*k+1)*(n-k)!));
%Y A381999 Cf. A336950, A381997, A381998, A382000, A382001.
%Y A381999 Cf. A001764, A364983, A371318.
%K A381999 nonn
%O A381999 0,3
%A A381999 _Seiichi Manyama_, Mar 12 2025