Diagonal sums of a binomial number triangle.

Terms

a(0) =1a(1) =1a(2) =4a(3) =12a(4) =42a(5) =149a(6) =543a(7) =2007a(8) =7501a(9) =28265a(10) =107196a(11) =408653a(12) =1564506a(13) =6010964a(14) =23164467a(15) =89501021a(16) =346588092a(17) =1344804060a(18) =5227147969a(19) =20349230347a(20) =79330194097a(21) =309653982738