a(n) = Sum_{k=0..n} fibonomial(k+3,3), n >= 0.

Terms

a(0) =1a(1) =4a(2) =19a(3) =79a(4) =339a(5) =1431a(6) =6072a(7) =25707a(8) =108922a(9) =461362a(10) =1954426a(11) =8278978a(12) =35070483a(13) =148560678a(14) =629313573a(15) =2665814361a(16) =11292572005a(17) =47836100785a(18) =202636977730a(19) =858384007525