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 A379700 #8 Dec 30 2024 10:50:18
%S A379700 1,4,45,889,25613,977271,46586281,2669066695,178800270009,
%T A379700 13720918482235,1187217400278941,114379273346497611,
%U A379700 12144899525595998821,1409261040317551952935,177436990866294436727409,24094164269339964351367231,3510079015962779901366174449,546103202348225740056486964467
%N A379700 Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-x) / (1 + 3*x*exp(x)) ).
%F A379700 a(n) = (n!/(n+1)) * Sum_{k=0..n} 3^(n-k) * (2*n-k+1)^k * binomial(n+1,n-k)/k!.
%o A379700 (PARI) a(n) = n!*sum(k=0, n, 3^(n-k)*(2*n-k+1)^k*binomial(n+1, n-k)/k!)/(n+1);
%Y A379700 Cf. A379456, A379699.
%Y A379700 Cf. A377374.
%K A379700 nonn
%O A379700 0,2
%A A379700 _Seiichi Manyama_, Dec 30 2024