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 A380157 #8 Jan 14 2025 01:49:16
%S A380157 1,1,4,1,-44,265,2458,-48419,-99320,12598417,-82133810,-4205894891,
%T A380157 86494587292,1457086105657,-79743685096670,-88062957588275,
%U A380157 77425160027442832,-1138977883460384735,-76951663963327663082,2978943480750081242629,64353221406902873516260
%N A380157 Expansion of e.g.f. (1 + 3*x*exp(3*x))^(1/3).
%F A380157 a(n) = 3^n * n! * Sum_{k=0..n} k^(n-k) * binomial(1/3,k)/(n-k)!.
%F A380157 a(n) == 1 (mod 3).
%o A380157 (PARI) a(n) = 3^n*n!*sum(k=0, n, k^(n-k)*binomial(1/3, k)/(n-k)!);
%Y A380157 Cf. A191498, A380134.
%K A380157 sign
%O A380157 0,3
%A A380157 _Seiichi Manyama_, Jan 13 2025