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 A376123 #12 Sep 11 2024 10:04:39
%S A376123 0,1,6,69,1216,29145,886176,32692597,1419067392,70867571409,
%T A376123 4002985561600,252350116482981,17564151708647424,1337849793390444841,
%U A376123 110694246048458612736,9886625352559043695125,948044647019001482838016,97146789899768662622795553
%N A376123 E.g.f. A(x) satisfies A(x) = x * exp(A(x)) * (1 + 2*A(x)).
%H A376123 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376123 E.g.f.: Series_Reversion( x * exp(-x) / (1 + 2*x) ).
%F A376123 a(n) = n! * Sum_{k=1..n} 2^(n-k) * n^(k-1) * binomial(n-1,k-1)/k!.
%F A376123 a(n) = n * A088692(n-1).
%F A376123 a(n) ~ 2^(2*n) * n^(n-1) / (sqrt(3) * exp(n/2)). - _Vaclav Kotesovec_, Sep 11 2024
%o A376123 (PARI) a(n) = n!*sum(k=1, n, 2^(n-k)*n^(k-1)*binomial(n-1, k-1)/k!);
%Y A376123 Cf. A052885, A376124.
%Y A376123 Cf. A088692, A376093, A376100.
%K A376123 nonn
%O A376123 0,3
%A A376123 _Seiichi Manyama_, Sep 11 2024