a(n) = Sum_{k=0..n} T(n, k), array T as in A047080.

Terms

a(0) =1a(1) =2a(2) =3a(3) =6a(4) =11a(5) =20a(6) =37a(7) =68a(8) =125a(9) =230a(10) =423a(11) =778a(12) =1431a(13) =2632a(14) =4841a(15) =8904a(16) =16377a(17) =30122a(18) =55403a(19) =101902a(20) =187427a(21) =344732a(22) =634061a(23) =1166220a(24) =2145013a(25) =3945294a(26) =7256527a(27) =13346834a(28) =24548655a(29) =45152016