a(n) = Sum_{k=0..n} binomial(2*n+k+1,n-k).

Terms

a(0) =1a(1) =4a(2) =17a(3) =73a(4) =314a(5) =1350a(6) =5798a(7) =24872a(8) =106573a(9) =456169a(10) =1950697a(11) =8334539a(12) =35582783a(13) =151809737a(14) =647279131a(15) =2758310121a(16) =11748383530a(17) =50017026766a(18) =212853648914a(19) =905491551372