[seqfan] A family of polynomials

[Benoit Cloitre]

Hi,

I recently came across polynomials P_(n,k) of degree n and depending on 2
paramaters (n,k). So far I didn't see the pattern using the OEIS. I listed
below the polynomials P(n,k) I succeeded to find by experiments and it is
hard to compute more of them. Someone can see a rule behind this? Thanks in
advance.

Benoit

P_(1,1)(x)=8*x+32
P_(2,2)(x)=16*x^2+184*x+360
P_(3,3)(x)=32*x^3+720*x^2+4072*x+5352
P_(4,4)(x)=64*x^4+2368*x^3+26288*x^2+99128*x+99768

P_(2,1)(x)=8*x^2+80*x+32
P_(3,2)(x)=16*x^3+336*x^2+1760*x+2136
P_(4,3)(x)=32*x^4 + 1136*x^3 + 12064*x^2 + 43456*x + 41856

P_(3,1)(x)=16/3*x^3 +96*x^2+1280/3*x+448
P_(4,2)(x)=32/3*x^4+1040/3*x^3+10048/3*x^2+32896/3*x+9680

P_(4,1)(x)=8/3*x^4+224/3*x^3+1864/3*x^2+5344/3*x+1412
P_(5,2)(x)=16/3*x^5+736/3*x^4+11168/3*x^3+68288/3*x^2+54344*x+38544

P_(5,1)(x)=16/15*x^5+128/3*x^4+1696/3*x^3+9184/3*x^2+32968/5*x+4320