a(n) = p(5n+4)/5 where p(k) denotes the k-th partition number.

Terms

a(0) =1a(1) =6a(2) =27a(3) =98a(4) =315a(5) =913a(6) =2462a(7) =6237a(8) =15035a(9) =34705a(10) =77231a(11) =166364a(12) =348326a(13) =710869a(14) =1417900a(15) =2769730a(16) =5308732a(17) =9999185a(18) =18533944a(19) =33845975a(20) =60960273a(21) =108389248a(22) =190410133a(23) =330733733a(24) =568388100a(25) =967054374a(26) =1629808139a(27) =2722189979