a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(2*k+1,2*n-4*k).

Terms

a(0) =1a(1) =0a(2) =1a(3) =6a(4) =1a(5) =20a(6) =21a(7) =42a(8) =141a(9) =128a(10) =505a(11) =782a(12) =1465a(13) =3852a(14) =5501a(15) =14290a(16) =26053a(17) =49464a(18) =113313a(19) =195446a(20) =433585a(21) =841732a(22) =1629285a(23) =3477754a(24) =6520445a(25) =13583472a(26) =26955209a(27) =52921182a(28) =109117737a(29) =212250492