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

Terms

a(0) =1a(1) =1a(2) =1a(3) =3a(4) =5a(5) =7a(6) =15a(7) =29a(8) =49a(9) =95a(10) =187a(11) =345a(12) =659a(13) =1289a(14) =2465a(15) =4739a(16) =9237a(17) =17911a(18) =34715a(19) =67705a(20) =132063a(21) =257477a(22) =503309a(23) =984983a(24) =1927895a(25) =3778017a(26) =7411237a(27) =14544967a(28) =28565661a(29) =56144615