Numerator of sum of numbers in set g(n) generated as in Comments.

Terms

a(0) =0a(1) =1a(2) =5a(3) =19a(4) =69a(5) =235a(6) =789a(7) =2603a(8) =8533a(9) =27819a(10) =90453a(11) =293547a(12) =951637a(13) =3082923a(14) =9983317a(15) =32320171a(16) =104617301a(17) =338602667a(18) =1095849301a(19) =3546458795a(20) =11477013845a(21) =37141260971a(22) =120193373525a(23) =388957383339