a(n) = E(k)*C(n+k,k) = Euler(k)*binomial(n+k,k) for k=4.

Terms

a(0) =5a(1) =25a(2) =75a(3) =175a(4) =350a(5) =630a(6) =1050a(7) =1650a(8) =2475a(9) =3575a(10) =5005a(11) =6825a(12) =9100a(13) =11900a(14) =15300a(15) =19380a(16) =24225a(17) =29925a(18) =36575a(19) =44275a(20) =53130a(21) =63250a(22) =74750a(23) =87750a(24) =102375a(25) =118755a(26) =137025a(27) =157325a(28) =179800a(29) =204600