Maximal matchings in rooted plane trees on n nodes.

Terms

a(0) =1a(1) =1a(2) =4a(3) =12a(4) =44a(5) =175a(6) =718a(7) =3052a(8) =13308a(9) =59139a(10) =266974a(11) =1220879a(12) =5643562a(13) =26327769a(14) =123793450a(15) =586078393a(16) =2791408028a(17) =13365916545a(18) =64302770488a(19) =310672722803