a(n) = m*(m+1)/2, where m = floor(n^(5/2)).

Terms

a(0) =1a(1) =15a(2) =120a(3) =528a(4) =1540a(5) =3916a(6) =8385a(7) =16471a(8) =29646a(9) =50086a(10) =80601a(11) =124251a(12) =185745a(13) =269011a(14) =379756a(15) =524800a(16) =709836a(17) =944625a(18) =1237951a(19) =1599366a(20) =2041210a(21) =2577585a(22) =3216916a(23) =3980431a(24) =4884375a(25) =5939181a(26) =7172578a(27) =8605026a(28) =10253656a(29) =12149985