a(n) = (n+1)*(n+2)*(n+3)*(n+12)*3^n/72.

Terms

a(0) =1a(1) =13a(2) =105a(3) =675a(4) =3780a(5) =19278a(6) =91854a(7) =415530a(8) =1804275a(9) =7577955a(10) =30961359a(11) =123589557a(12) =483611310a(13) =1860043500a(14) =7046907660a(15) =26344593252a(16) =97328636181a(17) =355781149065