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a(n) = Sum_{k=1..n} k! * k^(n-2) * |Stirling1(n,k)|.
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%I #9 Jun 20 2024 11:08:46

%S 0,1,3,32,802,36854,2698598,288450168,42388536888,8198703649296,

%T 2019226648157472,616991110153816848,229048514514263311008,

%U 101540936651344709359632,52984383824921037875927760,32145394332240602286960456192

%N a(n) = Sum_{k=1..n} k! * k^(n-2) * |Stirling1(n,k)|.

%F E.g.f.: Sum_{k>=1} (-log(1 - k*x))^k / k^2.

%o (PARI) a(n) = sum(k=1, n, k!*k^(n-2)*abs(stirling(n, k, 1)));

%Y Cf. A320096, A373855, A373870.

%Y Cf. A220181, A373873, A373874.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jun 20 2024