a(n) = 2^n * Sum_{k=0..n} Product_{j=1..k} (2/j)^((-1)^j).

Terms

a(0) =1a(1) =3a(2) =8a(3) =22a(4) =50a(5) =130a(6) =280a(7) =700a(8) =1470a(9) =3570a(10) =7392a(11) =17556a(12) =36036a(13) =84084a(14) =171600a(15) =394680a(16) =802230a(17) =1823250a(18) =3695120a(19) =8314020a(20) =16812796a(21) =37505468a(22) =75716368a(23) =167657672a(24) =338019500a(25) =743642900a(26) =1497686400a(27) =3276189000a(28) =6592494600a(29) =14348370600