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 A331797 #8 Jan 26 2020 17:48:25
%S A331797 0,1,5,28,183,1401,12466,127443,1478581,19239274,277797577,4409962349,
%T A331797 76355817104,1432117088325,28925947345561,625973017346996,
%U A331797 14449435509751843,354384392492622789,9202836581079864186,252260861877820739167,7278710020682729662089
%N A331797 E.g.f.: (exp(x) - 1) * exp(exp(x) - 1) / (2 - exp(x)).
%C A331797 Stirling transform of A007526.
%F A331797 a(n) = Sum_{k=0..n} Stirling2(n,k) * A007526(k).
%F A331797 a(n) = Sum_{k=1..n} binomial(n,k) * A000670(k) * A000110(n-k).
%F A331797 a(n) ~ n! * exp(1) / (2 * (log(2))^(n+1)). - _Vaclav Kotesovec_, Jan 26 2020
%t A331797 nmax = 20; CoefficientList[Series[(Exp[x] - 1) Exp[Exp[x] - 1]/(2 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A331797 A007526[n_] := n! Sum[1/k!, {k, 0, n - 1}]; a[n_] := Sum[StirlingS2[n, k] A007526[k], {k, 0, n}]; Table[a[n], {n, 0, 20}]
%t A331797 Table[(1/2) Sum[Binomial[n, k] HurwitzLerchPhi[1/2, -k, 0] BellB[n - k], {k, 1, n}], {n, 0, 20}]
%Y A331797 Cf. A000110, A000670, A007526, A059099, A331796, A331798.
%K A331797 nonn
%O A331797 0,3
%A A331797 _Ilya Gutkovskiy_, Jan 26 2020