a(n) is the nearest integer to binomial(n,n/2) = n!/((n/2)!)^2.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =6a(5) =11a(6) =20a(7) =37a(8) =70a(9) =132a(10) =252a(11) =482a(12) =924a(13) =1778a(14) =3432a(15) =6639a(16) =12870a(17) =24994a(18) =48620a(19) =94716a(20) =184756a(21) =360821a(22) =705432a(23) =1380533a(24) =2704156a(25) =5301248a(26) =10400600a(27) =20419624a(28) =40116600a(29) =78861995