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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 11:08:41

%S 0,1,1,8,142,4534,229658,16951416,1718394312,229119947280,

%T 38881745126112,8183542269446928,2092128552508587360,

%U 638590833851037194256,229398149222697428624688,95801846241560025353728512,46025711723325944648182502016

%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)*stirling(n, k, 1));

%Y Cf. A320083, A373857, A373869.

%Y Cf. A220181, A373873, A373875.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jun 20 2024