a(n) = CatalanNumber(n+1)*n*(3*n^2+5*n+2)/((4+n)*(3+n)).

Terms

a(0) =0a(1) =1a(2) =8a(3) =44a(4) =210a(5) =935a(6) =4004a(7) =16744a(8) =68952a(9) =281010a(10) =1136960a(11) =4576264a(12) =18349630a(13) =73370115a(14) =292746300a(15) =1166182800a(16) =4639918800a(17) =18443677230a(18) =73261092240a(19) =290845019400