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 A334191 #7 Apr 18 2020 11:49:48
%S A334191 1,0,-3,-9,0,189,1377,4374,-26001,-560601,-4999482,-18631053,
%T A334191 235966365,5966310960,71037580689,407585191059,-3965310883512,
%U A334191 -157871090202975,-2631946996862451,-24922384546473810,45577755305571339,7795795206234609027,192159735553383097014
%N A334191 a(n) = exp(1/3) * Sum_{k>=0} (3*k + 1)^n / ((-3)^k * k!).
%F A334191 G.f.: (1/(1 - x)) * Sum_{k>=0} (-x/(1 - x))^k / Product_{j=1..k} (1 - 3*j*x/(1 - x)).
%F A334191 E.g.f.: exp(x + (1 - exp(3*x)) / 3).
%t A334191 nmax = 22; CoefficientList[Series[1/(1 - x) Sum[(-x/(1 - x))^k/Product[(1 - 3 j x/(1 - x)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%t A334191 nmax = 22; CoefficientList[Series[Exp[x + (1 - Exp[3 x])/3], {x, 0, nmax}], x] Range[0, nmax]!
%t A334191 Table[Sum[Binomial[n, k] * 3^k * BellB[k, -1/3], {k, 0, n}], {n, 0, 22}] (* _Vaclav Kotesovec_, Apr 18 2020 *)
%Y A334191 Column k=3 of A334192.
%Y A334191 Cf. A003575, A293037, A317996, A334190.
%K A334191 sign
%O A334191 0,3
%A A334191 _Ilya Gutkovskiy_, Apr 18 2020