%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