A double binomial sum.

Terms

a(0) =1a(1) =2a(2) =5a(3) =18a(4) =69a(5) =306a(6) =1497a(7) =7890a(8) =45033a(9) =273474a(10) =1760301a(11) =11961522a(12) =85265325a(13) =636026418a(14) =4947725889a(15) =40019230386a(16) =335868650577