a(n) = Sum{T(i,j)}, 0<=j<=i, 0<=i<=n, T given by A026568.

Terms

a(0) =1a(1) =3a(2) =8a(3) =20a(4) =50a(5) =125a(6) =314a(7) =792a(8) =2003a(9) =5079a(10) =12897a(11) =32798a(12) =83478a(13) =212657a(14) =542040a(15) =1382376a(16) =3526916a(17) =9001805a(18) =22982298a(19) =58691692a(20) =149919707a(21) =383028163a(22) =978768731a(23) =2501494110a(24) =6394118165a(25) =16346237219a(26) =41793150985a(27) =106865638630