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

Terms

a(0) =1a(1) =0a(2) =5a(3) =7a(4) =45a(5) =121a(6) =533a(7) =1800a(8) =7157a(9) =26239a(10) =101640a(11) =384583a(12) =1483925a(13) =5693247a(14) =22013059a(15) =85076183a(16) =330014421a(17) =1281349195a(18) =4985766650a(19) =19422653367a(20) =75775163028a(21) =295953650376