a(n) = p(0) + p(1) + ... + p(n) - n - 1, where p = partition numbers, A000041.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =7a(5) =13a(6) =23a(7) =37a(8) =58a(9) =87a(10) =128a(11) =183a(12) =259a(13) =359a(14) =493a(15) =668a(16) =898a(17) =1194a(18) =1578a(19) =2067a(20) =2693a(21) =3484a(22) =4485a(23) =5739a(24) =7313a(25) =9270a(26) =11705a(27) =14714a(28) =18431a(29) =22995