A(k,3) where A(k,n) = Sum_{m=1..k} (-1)^(m+1) *binomial(n,m)*m^k.

Terms

a(0) =3a(1) =-9a(2) =6a(3) =36a(4) =150a(5) =540a(6) =1806a(7) =5796a(8) =18150a(9) =55980a(10) =171006a(11) =519156a(12) =1569750a(13) =4733820a(14) =14250606a(15) =42850116a(16) =128746950a(17) =386634060a(18) =1160688606a(19) =3483638676a(20) =10454061750a(21) =31368476700a(22) =94118013006a(23) =282379204836a(24) =847187946150