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

Terms

a(0) =1a(1) =2a(2) =9a(3) =34a(4) =104a(5) =326a(6) =995a(7) =2954a(8) =8671a(9) =25156a(10) =72256a(11) =205948a(12) =583109a(13) =1641570a(14) =4598725a(15) =12827750a(16) =35646792a(17) =98726370a(18) =272611239a(19) =750730314a(20) =2062369787a(21) =5653126280a(22) =15464460608a(23) =42225863096a(24) =115102499721a(25) =313264141570a(26) =851348070593