a(n) = Sum_{k=0..floor(n/5)} binomial(n,5*k)*binomial(6*k,k)/(5*k+1).

Terms

a(0) =1a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =7a(7) =22a(8) =57a(9) =127a(10) =259a(11) =529a(12) =1189a(13) =3004a(14) =8009a(15) =21073a(16) =53233a(17) =129813a(18) =312733a(19) =763573a(20) =1915251a(21) =4914736a(22) =12720841a(23) =32800186a(24) =83869501a(25) =213261712a(26) =542609237a(27) =1388542312a(28) =3579043987a(29) =9273567337