Solution (a(n)) of the complementary equation in Comments.

Terms

a(0) =1a(1) =6a(2) =15a(3) =29a(4) =50a(5) =79a(6) =117a(7) =165a(8) =224a(9) =295a(10) =379a(11) =477a(12) =591a(13) =722a(14) =871a(15) =1039a(16) =1227a(17) =1436a(18) =1667a(19) =1921a(20) =2199a(21) =2502a(22) =2831a(23) =3187a(24) =3571a(25) =3985a(26) =4430a(27) =4907a(28) =5417a(29) =5961