a(n) = binomial(floor(n*(sqrt(5)+3)/2), n) for n>=0.

Terms

a(0) =1a(1) =2a(2) =10a(3) =35a(4) =210a(5) =1287a(6) =5005a(7) =31824a(8) =125970a(9) =817190a(10) =5311735a(11) =21474180a(12) =141120525a(13) =927983760a(14) =3796297200a(15) =25140840660a(16) =103077446706a(17) =686353797976