Dirichlet g.f.: Product_{k>=2} 1 / (1 - k^(-s))^binomial(k+3,4).

Terms

a(0) =1a(1) =5a(2) =15a(3) =50a(4) =70a(5) =201a(6) =210a(7) =540a(8) =615a(9) =1065a(10) =1001a(11) =2745a(12) =1820a(13) =3430a(14) =4110a(15) =6751a(16) =4845a(17) =10950a(18) =7315a(19) =15930a(20) =13776a(21) =17655a(22) =14950a(23) =38775a(24) =22960a(25) =32851a(26) =35510a(27) =53865a(28) =35960a(29) =81015