a(n) = maximal value of C(i, j) * C(n-j, n-i) for 0 <= j <= i <= n.

Terms

a(0) =1a(1) =2a(2) =4a(3) =9a(4) =18a(5) =40a(6) =100a(7) =225a(8) =525a(9) =1225a(10) =3136a(11) =7056a(12) =17640a(13) =44100a(14) =108900a(15) =261360a(16) =637065a(17) =1656369a(18) =4008004a(19) =10020010a(20) =25050025a(21) =64128064a(22) =155739584a(23) =393853824a(24) =1012766976a(25) =2538950544a(26) =6347376360a(27) =15868440900a(28) =41408180100a(29) =102252852900