a(n) = n! if n <= 3, otherwise a(n) = 2*(a(n-1) + a(n-3)) + a(n-2).

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =16a(5) =42a(6) =112a(7) =298a(8) =792a(9) =2106a(10) =5600a(11) =14890a(12) =39592a(13) =105274a(14) =279920a(15) =744298a(16) =1979064a(17) =5262266a(18) =13992192a(19) =37204778a(20) =98926280a(21) =263041722a(22) =699419280a(23) =1859732842a(24) =4944968408a(25) =13148508218a(26) =34961450528a(27) =92961346090a(28) =247181159144a(29) =657246565434