[seqfan] Addition to A125854

[Peter Luschny]

Max Alekseyev provided A125854(4) = 2001907169	
quite recently and added the comment
"No other terms below 10^10."

Max, how did you check this?

I observed:
A125854 := [3, 29, 37, 3373];
A := proc(n) local v; add((v+2)^(n-2)*binomial(n-1,v),v=0..n-1) end;
seq(modp(A(i),i), i = A125854); -> [0,0,0,0]

and found no others for several thousands checked.
Is this trivial? Does it extend to A125854(4)?

Thank you.
Peter Luschny