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

Terms

a(0) =1a(1) =3a(2) =12a(3) =50a(4) =211a(5) =895a(6) =3805a(7) =16193a(8) =68940a(9) =293526a(10) =1249622a(11) =5318976a(12) =22634700a(13) =96296410a(14) =409573584a(15) =1741574006a(16) =7403616923a(17) =31466106703a(18) =133704121665a(19) =568008916093