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 A350720 #18 Feb 04 2022 08:22:49
%S A350720 1,3,69,3948,422082,72567522,18304992558,6367730357160,
%T A350720 2921446409138136,1709074810258369776,1241694104839498851552,
%U A350720 1096850187800368469477424,1157691464039682741551221152,1438880771284303822650674399664
%N A350720 a(n) = Sum_{k=0..n} k! * 3^k * k^n * Stirling1(n,k).
%H A350720 Seiichi Manyama, <a href="/A350720/b350720.txt">Table of n, a(n) for n = 0..213</a>
%F A350720 E.g.f.: Sum_{k>=0} (3 * log(1 + k*x))^k.
%t A350720 a[0] = 1; a[n_] := Sum[k! * 3^k * k^n * StirlingS1[n, k], {k, 1, n}]; Array[a, 14, 0] (* _Amiram Eldar_, Feb 03 2022 *)
%o A350720 (PARI) a(n) = sum(k=0, n, k!*3^k*k^n*stirling(n, k, 1));
%o A350720 (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*log(1+k*x))^k)))
%Y A350720 Cf. A320083, A350719.
%Y A350720 Cf. A195263, A335531, A350721.
%K A350720 nonn
%O A350720 0,2
%A A350720 _Seiichi Manyama_, Feb 03 2022