Sequence equals its 4th differences shifted by one index.

Terms

a(0) =1a(1) =3a(2) =7a(3) =15a(4) =32a(5) =70a(6) =156a(7) =349a(8) =778a(9) =1728a(10) =3833a(11) =8505a(12) =18884a(13) =41943a(14) =93160a(15) =206897a(16) =459459a(17) =1020311a(18) =2265815a(19) =5031792a(20) =11174374a(21) =24815508a(22) =55108933a(23) =122382762a(24) =271780616a(25) =603555049a(26) =1340341377a(27) =2976555532a(28) =6610168495a(29) =14679492624