a(n) = n*F(n-1) + F(n), where F = A000045.

Terms

a(0) =0a(1) =1a(2) =3a(3) =5a(4) =11a(5) =20a(6) =38a(7) =69a(8) =125a(9) =223a(10) =395a(11) =694a(12) =1212a(13) =2105a(14) =3639a(15) =6265a(16) =10747a(17) =18376a(18) =31330a(19) =53277a(20) =90385a(21) =153011a(22) =258523a(23) =436010a(24) =734136a(25) =1234225a(26) =2072043a(27) =3474029a(28) =5817515a(29) =9730748