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 A308519 #5 Jun 03 2019 19:47:07
%S A308519 1,-1,1,0,-2,2,9,-24,-80,339,1127,-6438,-22051,179670,705969,-6316587,
%T A308519 -34059363,234694313,1788358694,-10539103220,-107105535812,
%U A308519 679821765685,9404735956848,-39383677719404,-965379929608361,375758547940149,86199829280567638,158307964563289211
%N A308519 Expansion of e.g.f. exp(exp(1 - exp(x)) - 1).
%C A308519 Exponential transform of A000587 (complementary Bell numbers).
%F A308519 a(n) = Sum_{k=0..n} (-1)^k*Stirling2(n,k)*A000110(k).
%F A308519 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1)*A000587(k)*a(n-k).
%t A308519 nmax = 27; CoefficientList[Series[Exp[Exp[1 - Exp[x]] - 1], {x, 0, nmax}], x] Range[0, nmax]!
%t A308519 Table[Sum[(-1)^k StirlingS2[n, k] BellB[k], {k, 0, n}], {n, 0, 27}]
%t A308519 a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] BellB[k, -1] a[n - k], {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 27}]
%Y A308519 Cf. A000110, A000258, A000587, A308518.
%K A308519 sign
%O A308519 0,5
%A A308519 _Ilya Gutkovskiy_, Jun 03 2019