G.f.: 1/((1-5x)(1-10x)(1-12x)).

Terms

a(0) =1a(1) =27a(2) =499a(3) =7863a(4) =113731a(5) =1561647a(6) =20724139a(7) =268611543a(8) =3422947891a(9) =43073421567a(10) =536871293179