a(n) = (n+1)*(n+2)^2*(n+3)*(11*n^3 + 58*n^2 + 101*n + 60)/720.

Terms

a(0) =1a(1) =23a(2) =194a(3) =985a(4) =3668a(5) =11074a(6) =28728a(7) =66438a(8) =140415a(9) =276001a(10) =511082a(11) =900263a(12) =1519882a(13) =2473940a(14) =3901024a(15) =5982300a(16) =8950653a(17) =13101051a(18) =18802210a(19) =26509637a(20) =36780128a(21) =50287798a(22) =67841720a(23) =90405250a(24) =119117115a(25) =155314341a(26) =200557098