a(n) = n^4/8 + (5*n^3)/12 - n^2/8 - (5*n)/12 + 1.

Terms

a(0) =1a(1) =1a(2) =1a(3) =5a(4) =20a(5) =56a(6) =126a(7) =246a(8) =435a(9) =715a(10) =1111a(11) =1651a(12) =2366a(13) =3290a(14) =4460a(15) =5916a(16) =7701a(17) =9861a(18) =12445a(19) =15505a(20) =19096a(21) =23276a(22) =28106a(23) =33650a(24) =39975a(25) =47151a(26) =55251a(27) =64351a(28) =74530a(29) =85870