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 A307362 #6 Apr 05 2019 17:46:49
%S A307362 1,1,5,43,569,10651,265985,8498323,336759449,16158195691,920970111665,
%T A307362 61390084384003,4724023128773129,415070770350493531,
%U A307362 41252331696522595745,4599993183150111332083,571422442346267636255609,78581827113539181495412171,11896744343184751608550862225
%N A307362 Expansion of e.g.f. Sum_{j>=0} (exp(x) - 1)^j / Product_{k=1..j} (1 - k*(exp(x) - 1)).
%F A307362 G.f.: Sum_{j>=0} j!*Bell(j)*x^j / Product_{k=1..j} (1 - k*x).
%F A307362 a(n) = Sum_{k=0..n} Stirling2(n,k)*k!*Bell(k).
%t A307362 nmax = 18; CoefficientList[Series[Sum[(Exp[x] - 1)^j/Product[(1 - k (Exp[x] - 1)), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
%t A307362 nmax = 18; CoefficientList[Series[Sum[j! BellB[j] x^j/Product[(1 - k x), {k, 1, j}], {j, 0, nmax}], {x, 0, nmax}], x]
%t A307362 Table[Sum[StirlingS2[n, k] k! BellB[k], {k, 0, n}], {n, 0, 18}]
%Y A307362 Cf. A000110, A000258, A000670, A137341, A307363.
%K A307362 nonn
%O A307362 0,3
%A A307362 _Ilya Gutkovskiy_, Apr 05 2019