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 A351424 #23 Feb 12 2022 02:41:59
%S A351424 1,0,3,-48,1270,-50375,2803829,-208616562,20003317746,-2402323535658,
%T A351424 353219463307920,-62411008199372327,13048469028962425266,
%U A351424 -3186116313706825820802,898478811755719496052919,-289795933163271680910773018,106008143082108931457543700504
%N A351424 a(n) = n! * [x^n] -log(1 - f^(n-1)(x)), where f(x) = log(1+x).
%H A351424 Seiichi Manyama, <a href="/A351424/b351424.txt">Table of n, a(n) for n = 1..247</a>
%F A351424 a(n) = T(n,n), T(n,k) = Sum_{j=1..n} Stirling1(n,j) * T(j,k-1), k>1, T(n,1) = (n-1)!.
%p A351424 g:= x-> log(1+x):
%p A351424 a:= n-> n! * coeff(series(-log(1-(g@@(n-1))(x)), x, n+1), x, n):
%p A351424 seq(a(n), n=1..19); # _Alois P. Heinz_, Feb 11 2022
%t A351424 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, n]; Array[a, 16] (* _Amiram Eldar_, Feb 11 2022 *)
%o A351424 (PARI) T(n, k) = if(k==1, (n-1)!, sum(j=1, n, stirling(n, j, 1)*T(j, k-1)));
%o A351424 a(n) = T(n, n);
%Y A351424 Main diagonal of A351420.
%Y A351424 Cf. A139383, A302358, A351433.
%K A351424 sign
%O A351424 1,3
%A A351424 _Seiichi Manyama_, Feb 11 2022