Sequence is its own 4th difference.

Terms

a(0) =1a(1) =2a(2) =7a(3) =26a(4) =95a(5) =345a(6) =1252a(7) =4544a(8) =16493a(9) =59864a(10) =217286a(11) =788674a(12) =2862617a(13) =10390321a(14) =37713313a(15) =136886433a(16) =496850954a(17) =1803399103a(18) =6545722210a(19) =23758733815a(20) =86236081273a(21) =313007493212