a(n) = n! * [x^n] (2*x - 4*exp(x) + 3*exp(2*x) + 3) / 2.

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =22a(5) =46a(6) =94a(7) =190a(8) =382a(9) =766a(10) =1534a(11) =3070a(12) =6142a(13) =12286a(14) =24574a(15) =49150a(16) =98302a(17) =196606a(18) =393214a(19) =786430a(20) =1572862a(21) =3145726a(22) =6291454a(23) =12582910a(24) =25165822a(25) =50331646a(26) =100663294a(27) =201326590a(28) =402653182a(29) =805306366