a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=i, T given by A026714.

Terms

a(0) =1a(1) =3a(2) =8a(3) =20a(4) =49a(5) =117a(6) =280a(7) =656a(8) =1551a(9) =3597a(10) =8442a(11) =19460a(12) =45457a(13) =104387a(14) =243086a(15) =556842a(16) =1294027a(17) =2959369a(18) =6867428a(19) =15687806a(20) =36368875a(21) =83015759a(22) =192321728a(23) =438755532a(24) =1015963203a(25) =2316887259a(26) =5363009706a(27) =12226893148a(28) =28295070847