G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k/(1-3*x)^k.

Terms

a(0) =1a(1) =1a(2) =2a(3) =8a(4) =32a(5) =122a(6) =462a(7) =1758a(8) =6718a(9) =25750a(10) =98956a(11) =381196a(12) =1471678a(13) =5693146a(14) =22064296a(15) =85655812a(16) =333035302a(17) =1296684130a(18) =5055195944a(19) =19731318068a(20) =77098776372a(21) =301561031472