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%I #4 Nov 27 2019 12:52:40
%S 0,1,2,9,41,233,1531,11537,98047,928529,9700111,110843729,1375599151,
%T 18427159889,265038487471,4074124514129,66660157879471,
%U 1156745432699729,21220242625821871,410344904191816529,8342603132569783471,177902207647600456529,3970574571687854263471
%N a(n) = Sum_{k=1..n} (-1)^(n - k) * H(k) * k!, where H(k) is the k-th harmonic number.
%F a(n) = Sum_{k=1..n} (-1)^(n - k) * |Stirling1(k+1,2)|.
%t Table[Sum[(-1)^(n - k) HarmonicNumber[k] k!, {k, 1, n}], {n, 0, 22}]
%Y Cf. A000254, A001008, A002805, A092692, A097422.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Nov 27 2019