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 A381998 #14 Mar 22 2025 09:58:11
%S A381998 1,1,8,90,1472,31920,865152,28197904,1075122176,46976064768,
%T A381998 2315080816640,127068467480064,7688296957870080,508450036968779776,
%U A381998 36490818871396499456,2824787199565881477120,234622076533699738861568,20813348299168251651883008,1964063064959266899440959488
%N A381998 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^2.
%F A381998 a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A000108(k)/(n-k)!.
%F A381998 From _Vaclav Kotesovec_, Mar 22 2025: (Start)
%F A381998 E.g.f.: 2/(1 + sqrt(1 - 4*exp(2*x)*x)).
%F A381998 a(n) ~ sqrt(1 + LambertW(1/2)) * 2^(n + 1/2) * n^(n-1) / (exp(n) * LambertW(1/2)^n). (End)
%o A381998 (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(2*k+1, k)/((2*k+1)*(n-k)!));
%Y A381998 Cf. A336950, A381997, A381999, A382000, A382001.
%Y A381998 Cf. A000108, A295238, A379885.
%K A381998 nonn
%O A381998 0,3
%A A381998 _Seiichi Manyama_, Mar 12 2025