a(n) = Sum_{i=0..n} T(i,n-i), array T as in A049735.

Terms

a(0) =1a(1) =10a(2) =35a(3) =100a(4) =197a(5) =366a(6) =603a(7) =896a(8) =1293a(9) =1850a(10) =2467a(11) =3236a(12) =4109a(13) =5198a(14) =6455a(15) =7880a(16) =9461a(17) =11290a(18) =13327a(19) =15644a(20) =18149a(21) =20886a(22) =23975a(23) =27312a(24) =30849a(25) =34826a(26) =39127a(27) =43740a(28) =48601a(29) =53910