a(n) = Sum_{k=0..floor((n-1)/4)} Stirling2(n,4*k+1).

Terms

a(0) =0a(1) =1a(2) =1a(3) =1a(4) =1a(5) =2a(6) =16a(7) =141a(8) =1051a(9) =6953a(10) =42571a(11) =247886a(12) =1401676a(13) =7868005a(14) =45210257a(15) =277899961a(16) =1917140421a(17) =15186484134a(18) =135259346092