a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240.

Terms

a(0) =1a(1) =12a(2) =66a(3) =245a(4) =714a(5) =1764a(6) =3864a(7) =7722a(8) =14355a(9) =25168a(10) =42042a(11) =67431a(12) =104468a(13) =157080a(14) =230112a(15) =329460a(16) =462213a(17) =636804a(18) =863170a(19) =1152921a(20) =1519518a(21) =1978460a(22) =2547480a(23) =3246750a(24) =4099095a(25) =5130216a(26) =6368922a(27) =7847371a(28) =9601320a(29) =11670384