G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^3 * x^k*(1-x)^(n-k).

Terms

a(0) =1a(1) =1a(2) =1a(3) =7a(4) =19a(5) =37a(6) =151a(7) =541a(8) =1477a(9) =4999a(10) =18277a(11) =58651a(12) =195001a(13) =694747a(14) =2380429a(15) =8091223a(16) =28449667a(17) =99709057a(18) =346212319a(19) =1217144833a(20) =4300487251a(21) =15137730889a(22) =53484426379a(23) =189831062953a(24) =673630230931