a(n) = 15120*(2*n)!/(n!*(n + 5)!); super ballot numbers, row 4 of A135573.

Terms

a(0) =126a(1) =42a(2) =36a(3) =45a(4) =70a(5) =126a(6) =252a(7) =546a(8) =1260a(9) =3060a(10) =7752a(11) =20349a(12) =55062a(13) =152950a(14) =434700a(15) =1260630a(16) =3721860a(17) =11165580a(18) =33982200a(19) =104778450a(20) =326908764a(21) =1031019948a(22) =3283989464a(23) =10555680420a(24) =34214964120a(25) =111768882792a(26) =367755678864