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%I #19 Jun 20 2024 14:46:56
%S 0,1,0,1,15,391,16275,999391,85314915,9682617631,1411532175075,
%T 257220473522431,57317980108103715,15338554965273810271,
%U 4855172557420679314275,1794588990417909081447871,766066194581899382513514915,374061220058388896558805473311
%N a(n) = Sum_{k=1..n} (-1)^(n-k) * k! * k^(n-3) * Stirling2(n,k).
%F E.g.f.: Sum_{k>=1} (1 - exp(-k*x))^k / k^3.
%F Sum_{k>=0} a(k+2) * x^k/k! = Sum_{k>=0} k * (1 - exp(-k*x))^k.
%o (PARI) a(n) = sum(k=1, n, (-1)^(n-k)*k!*k^(n-3)*stirling(n, k, 2));
%Y Cf. A373869, A373870, A373871.
%Y Cf. A092552, A220181.
%K nonn
%O 0,5
%A _Seiichi Manyama_, Jun 20 2024
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