%I #17 Feb 16 2022 04:12:35
%S 1,-3,16,-124,1270,-16243,249776,-4494334,92716855,-2158505443,
%T 55996266046,-1602132913687,50124833578256,-1702501170925098,
%U 62391472267252322,-2453892459756494459,103101294099324376489,-4608723131704380915202
%N Expansion of e.g.f. -log(1 - log(1 + log(1 + log(1 + log(1+x))))).
%F a(n) = T(n,5), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.
%t T[n_, 1] := (n - 1)!; T[n_, k_] := T[n, k] = Sum[StirlingS1[n, j] * T[j, k - 1], {j, 1, n}]; a[n_] := T[n, 5]; Array[a, 18] (* _Amiram Eldar_, Feb 11 2022 *)
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(-log(1-log(1+log(1+log(1+log(1+x)))))))
%o (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
%o a(n) = T(n, 5);
%Y Column k=5 of A351420.
%Y Cf. A000359, A351428.
%K sign
%O 1,2
%A _Seiichi Manyama_, Feb 11 2022
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