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

Terms

a(0) =1a(1) =6a(2) =17a(3) =58a(4) =188a(5) =570a(6) =1715a(7) =5074a(8) =14787a(9) =42676a(10) =122104a(11) =346804a(12) =979013a(13) =2749150a(14) =7684437a(15) =21393326a(16) =59346996a(17) =164112814a(18) =452535543a(19) =1244660906a(20) =3415404295a(21) =9352256360a(22) =25559520752a(23) =69730069352a(24) =189923821833a(25) =516517036214