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 A351433 #16 Feb 11 2022 12:05:35
%S A351433 1,-1,0,0,-2,-75,-3334,-192864,-14443260,-1372372623,-162009663365,
%T A351433 -23314158802286,-4022712394579207,-820399656345934444,
%U A351433 -195326656416326556562,-53709209673236813446542,-16896296201917398543629108,-6030879950631118091070849321
%N A351433 a(n) = n! * [x^n] 1/(1 + f^n(x)), where f(x) = exp(x) - 1.
%H A351433 Seiichi Manyama, <a href="/A351433/b351433.txt">Table of n, a(n) for n = 0..247</a>
%F A351433 a(n) = T(n,n), T(n,k) = Sum_{j=0..n} Stirling2(n,j) * T(j,k-1), k>1, T(n,0) = (-1)^n * n!.
%p A351433 g:= x-> exp(x)-1:
%p A351433 a:= n-> n! * coeff(series(1/(1+(g@@n)(x)), x, n+1), x, n):
%p A351433 seq(a(n), n=0..22); # _Alois P. Heinz_, Feb 11 2022
%t A351433 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, n]; Array[a, 17, 0] (* _Amiram Eldar_, Feb 11 2022 *)
%o A351433 (PARI) T(n, k) = if(k==0, (-1)^n*n!, sum(j=0, n, stirling(n, j, 2)*T(j, k-1)));
%o A351433 a(n) = T(n, n);
%Y A351433 Main diagonal of A351429.
%Y A351433 Cf. A139383, A302358, A351424.
%K A351433 sign
%O A351433 0,5
%A A351433 _Seiichi Manyama_, Feb 11 2022