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%I #10 Jun 20 2024 11:08:38
%S 0,1,3,31,765,34651,2502213,263824891,38248036725,7298877611371,
%T 1773652375115973,534749297993098651,195883403209280580885,
%U 85687658454617655817291,44120264185381411695106533,26413555571018242181844978811
%N a(n) = Sum_{k=1..n} k! * k^(n-2) * Stirling2(n,k).
%F E.g.f.: Sum_{k>=1} (exp(k*x) - 1)^k / k^2.
%o (PARI) a(n) = sum(k=1, n, k!*k^(n-2)*stirling(n, k, 2));
%Y Cf. A122399, A244585, A373871.
%Y Cf. A220181, A373874, A373875.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Jun 20 2024