a(n) = sigma(n!!) where n!! is A006882(n).

Terms

a(0) =1a(1) =1a(2) =3a(3) =4a(4) =15a(5) =24a(6) =124a(7) =192a(8) =1020a(9) =1920a(10) =12264a(11) =23040a(12) =159666a(13) =322560a(14) =2555280a(15) =5041344a(16) =40893840a(17) =90744192a(18) =761260368a(19) =1814883840a(20) =15732804296a(21) =38900010240a(22) =377587663200a(23) =933600245760