G.f.: Sum_{n>=0} [Sum_{k=0..n} C(n,k)^2*x^k]^2 * x^n.

Terms

a(0) =1a(1) =1a(2) =3a(3) =10a(4) =37a(5) =140a(6) =544a(7) =2181a(8) =8873a(9) =36647a(10) =152950a(11) =644313a(12) =2734648a(13) =11681428a(14) =50173541a(15) =216532005a(16) =938383331a(17) =4081653710a(18) =17811999929a(19) =77957939080a(20) =342099306436