a(n) = round(n^n/n!) where round(1/2)=0.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =11a(5) =26a(6) =65a(7) =163a(8) =416a(9) =1068a(10) =2756a(11) =7148a(12) =18614a(13) =48639a(14) =127463a(15) =334865a(16) =881658a(17) =2325751a(18) =6145597a(19) =16263866a(20) =43099804a(21) =114356611a(22) =303761260a(23) =807692035a(24) =2149632061a(25) =5726042115a(26) =15264691107a(27) =40722913454a(28) =108713644516a(29) =290404350963