a(n) = Sum_{k=0..floor((n-1)/5)} Stirling2(n,5*k+1).

Terms

a(0) =0a(1) =1a(2) =1a(3) =1a(4) =1a(5) =1a(6) =2a(7) =22a(8) =267a(9) =2647a(10) =22828a(11) =179489a(12) =1323719a(13) =9323744a(14) =63502440a(15) =422172752a(16) =2763863468a(17) =18017811013a(18) =119078265944a(19) =822495346707