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 A376124 #12 Sep 11 2024 10:04:45
%S A376124 0,1,8,117,2584,77245,2923776,134147881,7237959296,449153207001,
%T A376124 31518672486400,2468063119978621,213353171897306112,
%U A376124 20181854221412587093,2073632053555295657984,229977288184566078752625,27382787929802599713243136,3483970698377702965413968689
%N A376124 E.g.f. A(x) satisfies A(x) = x * exp(A(x)) * (1 + 3*A(x)).
%H A376124 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A376124 E.g.f.: Series_Reversion( x * exp(-x) / (1 + 3*x) ).
%F A376124 a(n) = n! * Sum_{k=1..n} 3^(n-k) * n^(k-1) * binomial(n-1,k-1)/k!.
%F A376124 a(n) ~ ((7 + sqrt(13))/2)^n * n^(n-1) / (13^(1/4) * exp((7 - sqrt(13))*n/6)). - _Vaclav Kotesovec_, Sep 11 2024
%o A376124 (PARI) a(n) = n!*sum(k=1, n, 3^(n-k)*n^(k-1)*binomial(n-1, k-1)/k!);
%Y A376124 Cf. A052885, A376123.
%Y A376124 Cf. A376094, A376101.
%K A376124 nonn
%O A376124 0,3
%A A376124 _Seiichi Manyama_, Sep 11 2024