a(n) = Sum_{k=1..n} abs(A375383(n, k)).

Terms

a(0) =1a(1) =3a(2) =4a(3) =6a(4) =10a(5) =16a(6) =26a(7) =52a(8) =108a(9) =240a(10) =574a(11) =1566a(12) =4542a(13) =14998a(14) =51080a(15) =193986a(16) =776946a(17) =3396530a(18) =15302498a(19) =75908634a(20) =384194222a(21) =2104919470a(22) =11853419616a(23) =71548745928a(24) =440446031112