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 A378092 #12 Aug 05 2025 06:35:28
%S A378092 1,2,11,118,1993,46386,1376059,49601014,2104366513,102717184546,
%T A378092 5670357524011,349304240222070,23754501885783673,1767641331001915474,
%U A378092 142868173684094891803,12463599550013379095926,1167281368458948415748833,116814664082977998388994370,12440156205235958837516345419
%N A378092 E.g.f. satisfies A(x) = exp( x * (1-x) * A(x)^2 ) / (1-x).
%H A378092 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LambertW-Function.html">Lambert W-Function</a>.
%F A378092 E.g.f.: exp( -LambertW(-2*x/(1-x))/2 )/(1-x).
%F A378092 a(n) = n! * Sum_{k=0..n} (2*k+1)^(k-1) * binomial(n,k)/k!.
%F A378092 a(n) ~ (1 + 2*exp(1))^(n + 3/2) * n^(n-1) / (2^(5/2) * exp(n+1)). - _Vaclav Kotesovec_, Aug 05 2025
%o A378092 (PARI) a(n) = n!*sum(k=0, n, (2*k+1)^(k-1)*binomial(n, k)/k!);
%Y A378092 Cf. A352410, A378093.
%Y A378092 Cf. A378041.
%K A378092 nonn
%O A378092 0,2
%A A378092 _Seiichi Manyama_, Nov 16 2024