Expansion of 1 + f/(1 + 2*f), where f is the g.f. of the swinging factorial (A056040).

Terms

a(0) =1a(1) =1a(2) =0a(3) =2a(4) =-10a(5) =30a(6) =-84a(7) =244a(8) =-722a(9) =2126a(10) =-6252a(11) =18364a(12) =-53988a(13) =158668a(14) =-466408a(15) =1370792a(16) =-4029154a(17) =11842222a(18) =-34806972a(19) =102303468a(20) =-300690348a(21) =883782404a(22) =-2597604952a(23) =7634834648a(24) =-22440207764a(25) =65955900268a(26) =-193856647736a(27) =569780485080