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

Terms

a(0) =1a(1) =3a(2) =9a(3) =46a(4) =171a(5) =591a(6) =2033a(7) =6714a(8) =21606a(9) =68308a(10) =212370a(11) =651234a(12) =1974113a(13) =5924277a(14) =17623671a(15) =52025858a(16) =152539077a(17) =444530073a(18) =1288396257a(19) =3715833732a(20) =10668907932a(21) =30507914696a(22) =86912853588a(23) =246755125332a(24) =698353551105