Sum of adjacent Catalan numbers.

Terms

a(0) =2a(1) =3a(2) =7a(3) =19a(4) =56a(5) =174a(6) =561a(7) =1859a(8) =6292a(9) =21658a(10) =75582a(11) =266798a(12) =950912a(13) =3417340a(14) =12369285a(15) =45052515a(16) =165002460a(17) =607283490a(18) =2244901890a(19) =8331383610a(20) =31030387440a(21) =115948830660a(22) =434542177290