a(n) = binomial(2*n, floor(n*sqrt(2))).

Terms

a(0) =1a(1) =2a(2) =6a(3) =15a(4) =56a(5) =120a(6) =495a(7) =2002a(8) =4368a(9) =18564a(10) =38760a(11) =170544a(12) =735471a(13) =1562275a(14) =6906900a(15) =14307150a(16) =64512240a(17) =131128140a(18) =600805296a(19) =2707475148a(20) =5586853480a(21) =25518731280a(22) =51915526432a(23) =239877544005