reviewed
approved
proposed
editing
a[n_] := Subfactorial[n]*Binomial[n + 1, 2];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Aug 18 2024 *)
E.g.f.: exp(-x)*x^2*(3 - 2*x + x^2)/(2*(1 - x)^3). - Ilya Gutkovskiy, Jun 25 2018
Cf. A000166, A000240, A000387,, A305730.