G.f.: 1 / Product_{n>=0} (1 - x^(n+4))^((n+1)*(n+2)*(n+3)/3!).

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =4a(6) =10a(7) =20a(8) =36a(9) =60a(10) =104a(11) =180a(12) =336a(13) =620a(14) =1174a(15) =2160a(16) =3961a(17) =7100a(18) =12690a(19) =22424a(20) =39651a(21) =69820a(22) =122970a(23) =215904a(24) =378470a(25) =660872a(26) =1150740a(27) =1996200a(28) =3452685a(29) =5952916