a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(2*n^2 + 6*n + 5)/720.

Terms

a(0) =1a(1) =26a(2) =250a(3) =1435a(4) =5978a(5) =19992a(6) =56952a(7) =143550a(8) =328515a(9) =695266a(10) =1379378a(11) =2591953a(12) =4650100a(13) =8015840a(14) =13344864a(15) =21546684a(16) =33857829a(17) =51929850a(18) =77934010a(19) =114684647a(20) =165783310a(21) =235785880a(22) =330395000a(23) =456680250a(24) =623328615a(25) =840927906a(26) =1122285906