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A373869 a(n) = Sum_{k=1..n} k! * k^(n-3) * Stirling1(n,k).

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%I A373869 #10 Jun 20 2024 11:11:54
%S A373869 0,1,0,2,26,674,28894,1848216,165229560,19698788448,3022496261616,
%T A373869 580460752264656,136441193196585408,38540172064949405616,
%U A373869 12883204327833557091984,5030833813902039858261504,2269484487197629285690675584,1171368942033975021150888242304
%N A373869 a(n) = Sum_{k=1..n} k! * k^(n-3) * Stirling1(n,k).
%F A373869 E.g.f.: Sum_{k>=1} log(1 + k*x)^k / k^3.
%o A373869 (PARI) a(n) = sum(k=1, n, k!*k^(n-3)*stirling(n, k, 1));
%Y A373869 Cf. A373870, A373871, A373872.
%Y A373869 Cf. A320083, A373857, A373874.
%K A373869 nonn
%O A373869 0,4
%A A373869 _Seiichi Manyama_, Jun 20 2024