a(n) = (1/4) * Sum_{k=0..floor(n/2)} (k+2) * binomial(2*k+2,2*n-4*k+1).

Terms

a(0) =1a(1) =0a(2) =3a(3) =3a(4) =6a(5) =20a(6) =16a(7) =70a(8) =85a(9) =190a(10) =399a(11) =565a(12) =1429a(13) =2114a(14) =4425a(15) =8145a(16) =13877a(17) =28508a(18) =47243a(19) =92523a(20) =165512a(21) =297396a(22) =562390a(23) =982140a(24) =1843714a(25) =3292870a(26) =5975118a(27) =10938740a(28) =19496065a(29) =35751958