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

Terms

a(0) =1a(1) =1a(2) =1a(3) =4a(4) =5a(5) =21a(6) =28a(7) =36a(8) =165a(9) =220a(10) =1001a(11) =1365a(12) =1820a(13) =8568a(14) =11628a(15) =54264a(16) =74613a(17) =346104a(18) =480700a(19) =657800a(20) =3108105a(21) =4292145a(22) =20160075a(23) =28048800a(24) =38567100a(25) =183579396a(26) =254186856a(27) =1203322288a(28) =1676056044a(29) =7898654920