Half the number of 0..n arrays of length 4 with second differences nonzero.

Terms

a(0) =5a(1) =27a(2) =99a(3) =252a(4) =546a(5) =1034a(6) =1803a(7) =2925a(8) =4517a(9) =6670a(10) =9528a(11) =13204a(12) =17869a(13) =23655a(14) =30763a(15) =39344a(16) =49626a(17) =61782a(18) =76067a(19) =92673a(20) =111885a(21) =133914a(22) =159072a(23) =187592a(24) =219813a(25) =255987a(26) =296483a(27) =341572a(28) =391650a(29) =447010