O16-065
> restart;
> pol:=proc(n)
> if n=0 then 2 elif n=1 then u else expand(u*pol(n-1)-pol(n-2)) fi end;
> 

  pol := proc(n)
    if n = 0 then 2
    elif n = 1 then u
    else expand(u*pol(n - 1) - pol(n - 2))
    fi
end

> cbes:=seq(pol(n),n=1..5);

                 2       3         4      2       5      3
     cbes := u, u  - 2, u  - 3 u, u  - 4 u  + 2, u  - 5 u  + 5 u

> plot([cbes],u=-2..2);

> seq(convert(1/pol(n),parfrac,u,complex),n=1..5);

                           1                             1
  1/u, -.3535533907 --------------- + .3535533907 ---------------,
                    u + 1.414213562               u - 1.414213562

                           1
        .1666666666 --------------- - .3333333331 1/u
                    u + 1.732050808

                              1                              1
         + .1666666666 ---------------, -.09567085812 ---------------
                       u - 1.732050808                u + 1.847759065

                              1                             1
         + .2309698833 --------------- - .2309698832 ---------------
                       u + .7653668647               u - .7653668647

                               1                             1
         + .09567085812 ---------------, .06180339880 ---------------
                        u - 1.847759065               u + 1.902113033

                              1
         - .1618033986 --------------- + .1999999997 1/u
                       u + 1.175570505

                              1                              1
         - .1618033987 --------------- + .06180339882 ---------------
                       u - 1.175570505                u - 1.902113033

> evalf(seq(sin((2*k+1)*Pi/10)/5,k=0..4));# OK pour la décomposition de P_5

  .06180339890, .1618033989, .2000000000, .1618033989, .06180339890

>