Least k such that Sum_{r=n+1..k} r >= n!.

Terms

a(0) =2a(1) =3a(2) =5a(3) =8a(4) =16a(5) =38a(6) =101a(7) =284a(8) =852a(9) =2694a(10) =8935a(11) =30952a(12) =111598a(13) =417560a(14) =1617204a(15) =6468816a(16) =26671611a(17) =113158064a(18) =493244565a(19) =2205856753a(20) =10108505545a(21) =47413093714a(22) =227385209453