a(n) is its own 4th difference.

Terms

a(0) =1a(1) =5a(2) =19a(3) =69a(4) =250a(5) =907a(6) =3292a(7) =11949a(8) =43371a(9) =157422a(10) =571388a(11) =2073943a(12) =7527704a(13) =27322992a(14) =99173120a(15) =359964521a(16) =1306548149a(17) =4742323107a(18) =17213011605a(19) =62477347458a(20) =226771411939a(21) =823102698260