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 A367743 #7 Nov 29 2023 11:37:37
%S A367743 1,-3,5,1,-7,-75,-99,1241,10161,18989,-332299,-3857551,-14440151,
%T A367743 141168997,2807256333,20182451657,-42073176479,-2999363709091,
%U A367743 -38439478980891,-161835672017439,3439471815545177,87228227501354517,937579822282327421,216540362854403513,-198501712690150659055
%N A367743 Expansion of e.g.f. exp(1 - x - exp(2*x)).
%F A367743 a(n) = exp(1) * Sum_{k>=0} (-1)^k * (2*k-1)^n / k!.
%F A367743 a(0) = 1; a(n) = -a(n-1) - Sum_{k=1..n} binomial(n-1,k-1) * 2^k * a(n-k).
%F A367743 a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * 2^k * A000587(k).
%t A367743 nmax = 24; CoefficientList[Series[Exp[1 - x - Exp[2 x]], {x, 0, nmax}], x] Range[0, nmax]!
%t A367743 a[0] = 1; a[n_] := a[n] = -a[n - 1] - Sum[Binomial[n - 1, k - 1] 2^k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
%t A367743 Table[Sum[(-1)^(n - k) Binomial[n, k] 2^k BellB[k, -1], {k, 0, n}], {n, 0, 24}]
%Y A367743 Cf. A000587, A004211, A009235, A109747, A124311, A126390, A308536, A308645, A367744.
%K A367743 sign
%O A367743 0,2
%A A367743 _Ilya Gutkovskiy_, Nov 29 2023