a(n) = Sum_{k=0..n} k^3 * 2^(n-k) * binomial(n,k).

Terms

a(0) =0a(1) =1a(2) =12a(3) =87a(4) =504a(5) =2565a(6) =11988a(7) =52731a(8) =221616a(9) =898857a(10) =3542940a(11) =13640319a(12) =51490728a(13) =191141613a(14) =699376356a(15) =2527001955a(16) =9030245472a(17) =31955015889a(18) =112093661484a(19) =390132432423