a(n) = Sum_{k=3..n} k*StirlingS2(n+1, k+1).

Terms

a(0) =3a(1) =34a(2) =260a(3) =1721a(4) =10808a(5) =67376a(6) =427449a(7) =2798432a(8) =19042144a(9) =135083103a(10) =999573770a(11) =7709458472a(12) =61890269371a(13) =516304085366