a(n) = [x^n] Product_{k=1..n} (1+x^k)^2 / x^k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =6a(4) =16a(5) =51a(6) =166a(7) =554a(8) =1896a(9) =6595a(10) =23212a(11) =82582a(12) =296393a(13) =1071738a(14) =3900696a(15) =14278074a(16) =52526972a(17) =194108087a(18) =720197524a(19) =2681854490a(20) =10019539112a(21) =37545876368a(22) =141080872362a(23) =531457445806