G.f.: Product_{j>=1} 1/(1-x^j)^binomial(j+4,4).

Terms

a(0) =1a(1) =5a(2) =30a(3) =145a(4) =660a(5) =2777a(6) =11160a(7) =42805a(8) =158490a(9) =568050a(10) =1980607a(11) =6735380a(12) =22402610a(13) =73022755a(14) =233692345a(15) =735350970a(16) =2278153310a(17) =6956560935a(18) =20958613740a(19) =62354061740a(20) =183332498533a(21) =533074229590