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 A351427 #13 Feb 16 2022 04:12:43
%S A351427 1,-1,-2,-4,-2,76,953,9103,77054,550457,2123247,-32551171,-1197444063,
%T A351427 -26019611323,-478608682879,-7915791047153,-115777452314939,
%U A351427 -1320533985179144,-3550854626237496,455708391448493954,21276221692251262984,703173682906460544467
%N A351427 Expansion of e.g.f. 1/exp(exp(exp(exp(x)-1)-1)-1).
%F A351427 a(n) = T(n,4), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.
%t A351427 T[n_, 0] := (-1)^n * n!; T[n_, k_] := T[n, k] = Sum[StirlingS2[n, j]*T[j, k - 1], {j, 0, n}]; a[n_] := T[n, 4]; Array[a, 22, 0] (* _Amiram Eldar_, Feb 11 2022 *)
%o A351427 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/exp(exp(exp(exp(x)-1)-1)-1)))
%o A351427 (PARI) T(n, k) = if(k==0, (-1)^n*n!, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
%o A351427 a(n) = T(n, 4);
%Y A351427 Column k=4 of A351429.
%Y A351427 Cf. A000587, A130410, A351428.
%Y A351427 Cf. A000307, A351422.
%K A351427 sign
%O A351427 0,3
%A A351427 _Seiichi Manyama_, Feb 11 2022