a(n)=Max{ (i+j)!/i!^2 | 0<=i,j<=n }.

Terms

a(0) =1a(1) =2a(2) =6a(3) =30a(4) =180a(5) =1260a(6) =10080a(7) =100800a(8) =1108800a(9) =13305600a(10) =172972800a(11) =2421619200a(12) =36324288000a(13) =617512896000