a(n) = Sum_{k=0..floor(n/4)} binomial(n+k-1,k) * binomial(k,n-4*k).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =4a(5) =5a(6) =0a(7) =0a(8) =36a(9) =90a(10) =55a(11) =0a(12) =364a(13) =1365a(14) =1680a(15) =680a(16) =3876a(17) =19380a(18) =35910a(19) =29260a(20) =51359a(21) =265650a(22) =657800a(23) =807300a(24) =966420a(25) =3681405a(26) =11044215a(27) =18123840a(28) =21993136a(29) =55141064