L.g.f.: Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(1-x)^(n-k).

Terms

a(0) =1a(1) =1a(2) =4a(3) =5a(4) =6a(5) =16a(6) =29a(7) =45a(8) =94a(9) =186a(10) =331a(11) =644a(12) =1275a(13) =2409a(14) =4644a(15) =9117a(16) =17630a(17) =34162a(18) =66843a(19) =130390a(20) =254153a(21) =497487a(22) =974166a(23) =1906860a(24) =3739131a(25) =7338839a(26) =14406214a(27) =28303525a(28) =55651262a(29) =109465176