thescoeffs ={45400};
theicoeffs ={2100};
thercoeffs ={2500};
a = .00001;
b = 1/14;
 For[k=2,k≤51,Sumthing=0; For[j = 1, j ≤ k-1, Sumthing = Sumthing + thescoeffs[[j]] theicoeffs[[k -j]]; j++] 
thescoeffs = Append[thescoeffs, -a Sumthing/(k-1)]; theicoeffs = Append[theicoeffs, -thescoeffs[[k]]-b theicoeffs[[k -1]]/(k-1)] ; thercoeffs = Append[thercoeffs, b/(k-1) theicoeffs[[k - 1]]];
 k++]

thescoeffs

theicoeffs

thercoeffs