a(n) is the sum of distinct sums of all subsets with two or more elements of {1, 2, ..., n}.

Terms

a(0) =0a(1) =0a(2) =3a(3) =18a(4) =52a(5) =117a(6) =228a(7) =403a(8) =663a(9) =1032a(10) =1537a(11) =2208a(12) =3078a(13) =4183a(14) =5562a(15) =7257a(16) =9313a(17) =11778a(18) =14703a(19) =18142a(20) =22152a(21) =26793a(22) =32128a(23) =38223a(24) =45147a(25) =52972a(26) =61773a(27) =71628a(28) =82618a(29) =94827