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

Terms

a(0) =1a(1) =1a(2) =5a(3) =20a(4) =81a(5) =335a(6) =1406a(7) =5965a(8) =25517a(9) =109872a(10) =475597a(11) =2067679a(12) =9022210a(13) =39490321a(14) =173311717a(15) =762382740a(16) =3360486897a(17) =14839284335a(18) =65632607150a(19) =290703303277