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

Terms

a(0) =0a(1) =1a(2) =8a(3) =45a(4) =216a(5) =945a(6) =3888a(7) =15309a(8) =58320a(9) =216513a(10) =787320a(11) =2814669a(12) =9920232a(13) =34543665a(14) =119042784a(15) =406552365a(16) =1377495072a(17) =4634696961a(18) =15496819560a(19) =51526925037a(20) =170465015160a(21) =561372288561