G.f.: [ Sum_{n>=0} (4*n)!/(n!)^4 * x^(4*n)/(1-x)^(4*n+4) ]^(1/4).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =7a(5) =31a(6) =91a(7) =211a(8) =997a(9) =5941a(10) =27181a(11) =97021a(12) =369907a(13) =1809211a(14) =9180991a(15) =40941031a(16) =170062027a(17) =753752971a(18) =3645183691a(19) =17473250251a(20) =79444369189a(21) =356738879533