A373857 - OEIS

%I #12 Jun 19 2024 09:28:13

%S 0,1,3,32,734,28994,1752046,150262104,17356844088,2597710341600,

%T 488957612319984,113044488306692304,31490845086661001664,

%U 10403092187976909854640,4021236906890850070201488,1798052050351216209712206336,920859156623446912386646303104

%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=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 (PARI) a(n) = sum(k=1, n, k!*k^(n-1)*stirling(n, k, 1));

%Y Cf. A092552, A244585, A373855.

%Y Cf. A320082, A320083.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 19 2024