a(n) = 1 + (9960 + (6804 + (2464 + (735 + (175 + (21 + n)*n)*n)*n)*n)*n)*n/5040.

Terms

a(0) =1a(1) =5a(2) =18a(3) =56a(4) =155a(5) =386a(6) =876a(7) =1836a(8) =3597a(9) =6655a(10) =11726a(11) =19812a(12) =32279a(13) =50948a(14) =78200a(15) =117096a(16) =171513a(17) =246297a(18) =347434a(19) =482240a(20) =659571a(21) =890054a(22) =1186340a(23) =1563380a(24) =2038725a(25) =2632851a(26) =3369510a(27) =4276108a(28) =5384111a(29) =6729480