Expansion of e.g.f. (tan x + sec x)^3.

Terms

a(0) =1a(1) =3a(2) =9a(3) =30a(4) =117a(5) =528a(6) =2709a(7) =15600a(8) =99657a(9) =699648a(10) =5355009a(11) =44382720a(12) =396019197a(13) =3785146368a(14) =38583663309a(15) =417826928640