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

Terms

a(0) =1a(1) =1a(2) =4a(3) =16a(4) =80a(5) =407a(6) =2221a(7) =12380a(8) =71196a(9) =417016a(10) =2484839a(11) =15001779a(12) =91603298a(13) =564661194a(14) =3509278042a(15) =21964437947a(16) =138330334357a(17) =875977578584