a(n) = Sum_{k=0..floor(n/4)} |Stirling1(n,4*k)|.

Terms

a(0) =1a(1) =0a(2) =0a(3) =0a(4) =1a(5) =10a(6) =85a(7) =735a(8) =6770a(9) =67320a(10) =724550a(11) =8427650a(12) =105615500a(13) =1420941600a(14) =20448793300a(15) =313670857500