a(n) = Sum_{k=0..n} Stirling2(n,k)*(1+(-1)^k)*2^k/2.

Terms

a(0) =1a(1) =0a(2) =4a(3) =12a(4) =44a(5) =220a(6) =1228a(7) =7196a(8) =45004a(9) =303900a(10) =2201676a(11) =16920860a(12) =136966860a(13) =1163989788a(14) =10364408140a(15) =96463232284a(16) =935872773068