a(n) = Sum_{i=0..2*n} Sum_{j=0..i} T(i, j), where T is given by A026552.

Terms

a(0) =1a(1) =4a(2) =13a(3) =31a(4) =85a(5) =193a(6) =517a(7) =1165a(8) =3109a(9) =6997a(10) =18661a(11) =41989a(12) =111973a(13) =251941a(14) =671845a(15) =1511653a(16) =4031077a(17) =9069925a(18) =24186469a(19) =54419557a(20) =145118821a(21) =326517349a(22) =870712933a(23) =1959104101a(24) =5224277605a(25) =11754624613a(26) =31345665637a(27) =70527747685