A polynomial coefficient sequence:p(x,n,m)=(1 + 4*Binomial[n, m]*x)^n.

Terms

a(0) =1a(1) =5a(2) =5a(3) =25a(4) =81a(5) =25a(6) =125a(7) =2197a(8) =2197a(9) =125a(10) =625a(11) =83521a(12) =390625a(13) =83521a(14) =625a(15) =3125a(16) =4084101a(17) =115856201a(18) =115856201a(19) =4084101a(20) =3125a(21) =15625a(22) =244140625a(23) =51520374361a(24) =282429536481a(25) =51520374361a(26) =244140625a(27) =15625a(28) =78125a(29) =17249876309