a(n) = Sum_{i=1..n} i^2*t(i), where t = A000217.

Terms

a(0) =1a(1) =13a(2) =67a(3) =227a(4) =602a(5) =1358a(6) =2730a(7) =5034a(8) =8679a(9) =14179a(10) =22165a(11) =33397a(12) =48776a(13) =69356a(14) =96356a(15) =131172a(16) =175389a(17) =230793a(18) =299383a(19) =383383a(20) =485254a(21) =607706a(22) =753710a(23) =926510a(24) =1129635a(25) =1366911a(26) =1642473a(27) =1960777a(28) =2326612a(29) =2745112