a(4n+k) = (k+1)*binomial(5n+k,n)/(4n+k+1), k=0..3.

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =3a(7) =4a(8) =5a(9) =11a(10) =18a(11) =26a(12) =35a(13) =80a(14) =136a(15) =204a(16) =285a(17) =665a(18) =1155a(19) =1771a(20) =2530a(21) =5980a(22) =10530a(23) =16380a(24) =23751a(25) =56637a(26) =100688a(27) =158224a(28) =231880a(29) =556512