a(n) = binomial(n,k(n)), where k(2) = 1, k(n) = k(n-1) + (a(n-1) mod 2).

Terms

a(0) =2a(1) =3a(2) =6a(3) =10a(4) =15a(5) =35a(6) =70a(7) =126a(8) =210a(9) =330a(10) =495a(11) =1287a(12) =3003a(13) =6435a(14) =12870a(15) =24310a(16) =43758a(17) =75582a(18) =125970a(19) =203490a(20) =319770a(21) =490314a(22) =735471a(23) =2042975a(24) =5311735a(25) =13037895a(26) =30421755a(27) =67863915a(28) =145422675a(29) =300540195