a(n) = (n+1)*(n+2)^2*(n+3)*(7*n^2 + 23*n + 20)/240.

Terms

a(0) =1a(1) =15a(2) =94a(3) =380a(4) =1176a(5) =3038a(6) =6888a(7) =14148a(8) =26895a(9) =48037a(10) =81510a(11) =132496a(12) =207662a(13) =315420a(14) =466208a(15) =672792a(16) =950589a(17) =1318011a(18) =1796830a(19) =2412564a(20) =3194884a(21) =4178042a(22) =5401320a(23) =6909500a(24) =8753355a(25) =10990161a(26) =13684230a(27) =16907464a(28) =20739930a(29) =25270456