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 A308536 #7 Jun 06 2019 21:59:43
%S A308536 1,-2,0,8,16,-64,-576,-1152,12800,136704,422912,-4464640,-72626176,
%T A308536 -413966336,1805123584,64448004096,651340611584,1132294045696,
%U A308536 -73000566390784,-1332193006190592,-10293724166750208,56984418960539648,3042980275005947904,46913652420264329216
%N A308536 Expansion of e.g.f. exp(1 - exp(2*x)).
%F A308536 O.g.f.: 1/(1 + 2*x/(1 - 2*x/(1 + 2*x/(1 - 4*x/(1 + 2*x/(1 - 6*x/(1 + 2*x/(1 - 8*x/(1 + ...))))))))), a continued fraction.
%F A308536 a(0) = 1; a(n) = -Sum_{k=1..n} 2^k*binomial(n-1,k-1)*a(n-k).
%F A308536 a(n) = exp(1) * 2^n * Sum_{k>=0} (-1)^k*k^n/k!.
%F A308536 a(n) = 2^n * A000587(n).
%t A308536 nmax = 23; CoefficientList[Series[Exp[1 - Exp[2x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A308536 a[n_] := a[n] = -Sum[2^k Binomial[n - 1, k - 1] a[n - k], {k, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]
%t A308536 Table[2^n BellB[n, -1], {n, 0, 23}]
%Y A308536 Cf. A000079, A000587, A009235, A055882, A213170.
%K A308536 sign
%O A308536 0,2
%A A308536 _Ilya Gutkovskiy_, Jun 06 2019