a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=n, T given by A026703.

Terms

a(0) =1a(1) =3a(2) =8a(3) =20a(4) =47a(5) =111a(6) =252a(7) =582a(8) =1303a(9) =2977a(10) =6618a(11) =15028a(12) =33269a(13) =75255a(14) =166152a(15) =374860a(16) =826115a(17) =1860407a(18) =4094612a(19) =9208832a(20) =20248703a(21) =45495079a(22) =99965896a(23) =224440544a(24) =492900919a(25) =1106034259a(26) =2428024608a(27) =5446009600a(28) =11951707547