Expansion of 1/(1+3*x*c(x)), c(x) the g.f. of Catalan numbers A000108.

Terms

a(0) =1a(1) =-3a(2) =6a(3) =-15a(4) =30a(5) =-78a(6) =144a(7) =-423a(8) =630a(9) =-2490a(10) =1956a(11) =-16998a(12) =-5844a(13) =-142860a(14) =-235740a(15) =-1475415a(16) =-3951450a(17) =-17627490a(18) =-57571740a(19) =-228692610a(20) =-810889020a(21) =-3098590020a(22) =-11377872720a(23) =-43011709110a(24) =-160518364740a(25) =-606261789828