a(n) = n! * Sum_{k=0..n-1} 4^k / k!.

Terms

a(0) =0a(1) =1a(2) =10a(3) =78a(4) =568a(5) =4120a(6) =30864a(7) =244720a(8) =2088832a(9) =19389312a(10) =196514560a(11) =2173194496a(12) =26128665600a(13) =339890756608