a(n) = binomial(3n+1, n-1).

Terms

a(0) =1a(1) =7a(2) =45a(3) =286a(4) =1820a(5) =11628a(6) =74613a(7) =480700a(8) =3108105a(9) =20160075a(10) =131128140a(11) =854992152a(12) =5586853480a(13) =36576848168a(14) =239877544005