a(n) = binomial(2*n-1,n) - binomial(n,2)*(binomial(n-1,2) + 2) - 1.

Terms

a(0) =0a(1) =0a(2) =0a(3) =4a(4) =45a(5) =281a(6) =1358a(7) =5790a(8) =23229a(9) =90667a(10) =350130a(11) =1348315a(12) =5194995a(13) =20051019a(14) =77548994a(15) =300527354a(16) =1166786517a(17) =4537546535a(18) =17672605394a(19) =68923231539a(20) =269128896899