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%I #10 Jun 19 2024 09:28:17
%S 0,1,5,80,2690,155074,13658386,1706098008,286888266696,62485391828448,
%T 17112247116585744,5755236604915060944,2331975856351260982848,
%U 1120439648590390138640304,629855675998212293917375344,409557081242059531918330384896
%N a(n) = Sum_{k=1..n} k! * k^(n-1) * |Stirling1(n,k)|.
%F E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k.
%t nmax=15; Range[0,nmax]!CoefficientList[Series[Sum[(-Log[1 - k*x])^k / k,{k,nmax}],{x,0,nmax}],x] (* _Stefano Spezia_, Jun 19 2024 *)
%o (PARI) a(n) = sum(k=1, n, k!*k^(n-1)*abs(stirling(n, k, 1)));
%Y Cf. A003713, A373856.
%Y Cf. A092552, A244585, A373857.
%Y Cf. A320096.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 19 2024