A transform of the Catalan numbers.

Terms

a(0) =1a(1) =1a(2) =3a(3) =5a(4) =12a(5) =24a(6) =56a(7) =123a(8) =291a(9) =677a(10) =1637a(11) =3954a(12) =9757a(13) =24171a(14) =60648a(15) =152929a(16) =388822a(17) =993216a(18) =2551808a(19) =6582899a(20) =17055507a(21) =44341141a(22) =115671498a(23) =302627130a(24) =793951897a(25) =2088103609a(26) =5504504961a(27) =14541271283a(28) =38489869502a(29) =102066761622