a(n) = Sum_{k>=0} k^n/2^k.

Terms

a(0) =2a(1) =2a(2) =6a(3) =26a(4) =150a(5) =1082a(6) =9366a(7) =94586a(8) =1091670a(9) =14174522a(10) =204495126a(11) =3245265146a(12) =56183135190