a(n) = Sum_{m=1..n, k=1..m} T(m,k), array T as in A049834.

Terms

a(0) =1a(1) =4a(2) =11a(3) =22a(4) =41a(5) =62a(6) =97a(7) =134a(8) =183a(9) =236a(10) =311a(11) =376a(12) =475a(13) =568a(14) =673a(15) =788a(16) =939a(17) =1066a(18) =1245a(19) =1398a(20) =1579a(21) =1772a(22) =2011a(23) =2202a(24) =2459a(25) =2708a(26) =2979a(27) =3240a(28) =3579a(29) =3842