a(n) = binomial(2*n-2, n-1) + (-1)^n.

Terms

a(0) =0a(1) =3a(2) =5a(3) =21a(4) =69a(5) =253a(6) =923a(7) =3433a(8) =12869a(9) =48621a(10) =184755a(11) =705433a(12) =2704155a(13) =10400601a(14) =40116599a(15) =155117521a(16) =601080389a(17) =2333606221a(18) =9075135299a(19) =35345263801a(20) =137846528819a(21) =538257874441