a(n) = Sum_{k=0..n} k!!*(n - k)!!.

Terms

a(0) =1a(1) =2a(2) =5a(3) =10a(4) =26a(5) =58a(6) =167a(7) =414a(8) =1324a(9) =3606a(10) =12729a(11) =37674a(12) =145578a(13) =463770a(14) =1944879a(15) =6614190a(16) =29852856a(17) =107616150a(18) =518782545a(19) =1970493210a(20) =10077228270a(21) =40125873690a(22) =216425656215a(23) =899557170750