Sum of successive integers in a row of length p(n) where p counts integer partitions.

Terms

a(0) =1a(1) =5a(2) =15a(3) =45a(4) =105a(5) =264a(6) =555a(7) =1221a(8) =2445a(9) =4935a(10) =9324a(11) =17941a(12) =32522a(13) =59400a(14) =104808a(15) =184569a(16) =315711a(17) =540540a(18) =902335a(19) =1504800a(20) =2462724a(21) =4014513a(22) =6444425a(23) =10316250a(24) =16283707a(25) =25610886a(26) =39841865a(27) =61720659a(28) =94687230a(29) =144731706