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 A382001 #14 Mar 22 2025 11:28:25
%S A382001 1,1,16,462,20672,1261400,97728672,9190016416,1016963389696,
%T A382001 129485497897728,18648682990461440,2997567408967391744,
%U A382001 531985786683988512768,103321584851593487961088,21798243872991807130685440,4964302861788729054456729600,1213816740632458735310221672448
%N A382001 E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^6.
%C A382001 In general, if k>1 and e.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^k, then a(n) ~ sqrt(k) * sqrt(1 + LambertW(2*(k-1)^(k-1)/k^k)) * 2^n * n^(n-1) / ((k-1)^(3/2) * exp(n) * LambertW(2*(k-1)^(k-1)/k^k)^n). - _Vaclav Kotesovec_, Mar 22 2025
%F A382001 a(n) = n! * Sum_{k=0..n} (2*k)^(n-k) * A002295(k)/(n-k)!.
%F A382001 a(n) ~ sqrt(3*(1 + LambertW(3125/23328))) * 2^(n + 1/2) * n^(n-1) / (5^(3/2) * exp(n) * LambertW(3125/23328)^n). - _Vaclav Kotesovec_, Mar 22 2025
%o A382001 (PARI) a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(6*k+1, k)/((6*k+1)*(n-k)!));
%Y A382001 Cf. A336950, A381997, A381998, A381999, A382000.
%Y A382001 Cf. A002295, A381989.
%K A382001 nonn
%O A382001 0,3
%A A382001 _Seiichi Manyama_, Mar 12 2025