a(n) = Sum_{k=0..n} binomial(k+4,4) * binomial(k,n-k)^2.

Terms

a(0) =1a(1) =5a(2) =20a(3) =95a(4) =400a(5) =1561a(6) =5915a(7) =21610a(8) =76585a(9) =265075a(10) =898622a(11) =2992235a(12) =9810290a(13) =31727815a(14) =101379175a(15) =320464280a(16) =1003259080a(17) =3113576320a(18) =9586763720a(19) =29305985800a(20) =88997753446a(21) =268642069750a(22) =806394498200