Defined in comments.

Terms

a(0) =3a(1) =1a(2) =31a(3) =28a(4) =365a(5) =514a(6) =4388a(7) =8220a(8) =53871a(9) =122284a(10) =673222a(11) =1748055a(12) =8535397a(13) =24383499a(14) =109449848a(15) =334783855a(16) =1415768769a(17) =4548229589a(18) =18434398665a(19) =61345927764a(20) =241210652738a(21) =823296868656