A modified version of Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =12a(5) =36a(6) =112a(7) =360a(8) =1184a(9) =3968a(10) =13504a(11) =46544a(12) =162144a(13) =570016a(14) =2019648a(15) =7204864a(16) =25856896a(17) =93288576a(18) =338167296a(19) =1231045376a(20) =4498577408a(21) =16496039936a(22) =60681046016a(23) =223860786432a(24) =828040881664