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 A373857 #12 Jun 19 2024 09:28:13
%S A373857 0,1,3,32,734,28994,1752046,150262104,17356844088,2597710341600,
%T A373857 488957612319984,113044488306692304,31490845086661001664,
%U A373857 10403092187976909854640,4021236906890850070201488,1798052050351216209712206336,920859156623446912386646303104
%N A373857 a(n) = Sum_{k=1..n} k! * k^(n-1) * Stirling1(n,k).
%F A373857 E.g.f.: Sum_{k>=1} log(1 + k*x)^k / k.
%t A373857 nmax=16; Range[0,nmax]!CoefficientList[Series[Sum[(Log[1 + k*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* _Stefano Spezia_, Jun 19 2024 *)
%o A373857 (PARI) a(n) = sum(k=1, n, k!*k^(n-1)*stirling(n, k, 1));
%Y A373857 Cf. A092552, A244585, A373855.
%Y A373857 Cf. A320082, A320083.
%K A373857 nonn
%O A373857 0,3
%A A373857 _Seiichi Manyama_, Jun 19 2024