a(n) = 13*binomial(2n,n-6)/(n+7).

Terms

a(0) =1a(1) =13a(2) =104a(3) =663a(4) =3705a(5) =19019a(6) =92092a(7) =427570a(8) =1924065a(9) =8454225a(10) =36463440a(11) =154969620a(12) =650872404a(13) =2707475148a(14) =11173706960a(15) =45812198536a(16) =186803188858a(17) =758201178306