a(n) = binomial(floor(n*(1+sqrt(2))),n) for n>=0.

Terms

a(0) =1a(1) =2a(2) =6a(3) =35a(4) =126a(5) =792a(6) =3003a(7) =11440a(8) =75582a(9) =293930a(10) =1961256a(11) =7726160a(12) =30421755a(13) =206253075a(14) =818809200a(15) =5567902560a(16) =22239974430a(17) =151584480450a(18) =608359048206