Asymptotic value of odd Catalan numbers mod 2^n.

Terms

a(0) =0a(1) =1a(2) =1a(3) =5a(4) =13a(5) =29a(6) =29a(7) =93a(8) =221a(9) =221a(10) =733a(11) =1757a(12) =3805a(13) =7901a(14) =7901a(15) =24285a(16) =57053a(17) =122589a(18) =122589a(19) =384733a(20) =384733a(21) =384733a(22) =2481885a(23) =2481885a(24) =10870493a(25) =10870493a(26) =10870493a(27) =10870493a(28) =145088221a(29) =413523677