a(n) = Sum_{k=1..n, m=1..k} T(m,k); array T as in A049828.

Terms

a(0) =0a(1) =0a(2) =1a(3) =2a(4) =7a(5) =10a(6) =20a(7) =32a(8) =46a(9) =62a(10) =95a(11) =116a(12) =157a(13) =202a(14) =248a(15) =298a(16) =372a(17) =444a(18) =543a(19) =626a(20) =723a(21) =834a(22) =992a(23) =1112a(24) =1260a(25) =1436a(26) =1617a(27) =1802a(28) =2045a(29) =2236