A373857 a(n) = Sum_{k=1..n} k! * k^(n-1) * Stirling1(n,k).
0, 1, 3, 32, 734, 28994, 1752046, 150262104, 17356844088, 2597710341600, 488957612319984, 113044488306692304, 31490845086661001664, 10403092187976909854640, 4021236906890850070201488, 1798052050351216209712206336, 920859156623446912386646303104
Offset: 0
Keywords
Programs
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Mathematica
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 *) -
PARI
a(n) = sum(k=1, n, k!*k^(n-1)*stirling(n, k, 1));
Formula
E.g.f.: Sum_{k>=1} log(1 + k*x)^k / k.