a(n) = Sum_{k>=0} (-1)^k*binomial(n,5*k+4).

Terms

a(0) =0a(1) =0a(2) =0a(3) =0a(4) =1a(5) =5a(6) =15a(7) =35a(8) =70a(9) =125a(10) =200a(11) =275a(12) =275a(13) =0a(14) =-1000a(15) =-3625a(16) =-9500a(17) =-21250a(18) =-42500a(19) =-76875a(20) =-124375a(21) =-171875a(22) =-171875a(23) =0a(24) =621875a(25) =2250000a(26) =5890625a(27) =13171875a(28) =26343750a(29) =47656250