a(n) = Sum_{k=0..n} (k+1) * T(n, k), with T given by A026300.

Terms

a(0) =1a(1) =3a(2) =11a(3) =38a(4) =129a(5) =429a(6) =1407a(7) =4563a(8) =14669a(9) =46823a(10) =148587a(11) =469226a(12) =1475669a(13) =4624437a(14) =14447703a(15) =45017082a(16) =139937301a(17) =434093367a(18) =1344076131a(19) =4154688864a(20) =12823246677a(21) =39524238741a(22) =121671304191a(23) =374126377473