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

Terms

a(0) =1a(1) =0a(2) =5a(3) =7a(4) =27a(5) =66a(6) =195a(7) =540a(8) =1547a(9) =4408a(10) =12663a(11) =36455a(12) =105325a(13) =305046a(14) =885573a(15) =2576007a(16) =7506675a(17) =21909720a(18) =64039119a(19) =187418205a(20) =549141249a(21) =1610708190a(22) =4729015305a(23) =13896677718a(24) =40870234629a(25) =120290710176a(26) =354292339625