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

Terms

a(0) =1a(1) =0a(2) =2a(3) =6a(4) =14a(5) =60a(6) =182a(7) =616a(8) =2166a(9) =7260a(10) =25322a(11) =87802a(12) =304850a(13) =1067248a(14) =3734152a(15) =13109856a(16) =46130214a(17) =162540060a(18) =573823712a(19) =2028534772a(20) =7180402614a(21) =25447716580a(22) =90282520770a(23) =320619948480